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Some Phases of the 
Psychology of 
Puzzle 
Learning 



J. HUDSON BALLARD 



SOME PHASES OF THE PSYCHOLOGY 
OF PUZZLE LEARNING 



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J. HUDSON BALLARD 



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Submitted in partial fulfillment of the requirements for the 
degree of Doctor of Philosophy at New York University 



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Digitized by the, Internet Archive 
in 2011 with funding from 
The Library of Congress 



http://www.archive.org/details/somephasesofpsycOOball 



Contents 

8 



Chapter I 



PAGE 



INTRODUCTORY 5 



Definition of a puzzle 
Classification of puzzles 
Value of puzzles 
General discussion of method 
Reasons for this study 



Chapter II. 

HISTORICAL and CRITICAL I0 

i. General 

2. Examination of Dr. Ruger's Monograph 

(A) Objective Report 

(B) Subjective Report 

Chapter III. 
FIRST EXPERIMENTAL SERIES 2 7 

The Correlation Between Puzzle Learning and School In- 
telligence 

1. Introductory and Explanatory 

2. Reagents 

3. Apparatus 

4. Conduct of the Experiments 

5. Method of Obtaining School Rating 

6. Method of Calculating Results 

7. Description of Results 

8. Summary of Results 
0. Conclusions 



Chapter IV. 

PAGE 

SECOND EXPERIMENTAL SERIES 56 

An Intensive Study of Puzzle Learning with Special Ref- 
erence to Individual Differences and Methods of Learning 

1. Apparatus 

2. Reagents 

3. Procedure 

(A) In General 

(B) In Particular 

4. Discussion of Results 

(A) Preliminary 

(B) Individual Differences Among Reagents 

(C) Methods of Learning 

(D) Report of Supplementary Tests 

(E) Individual Differences Among Puzzles 

(F) Discussion of Results in Control Experiments 

Chapter V. 

CONCLUDING DISCUSSION 86 

Conclusions 

Comparisons 

Suggestions 

BIBLIOGRAPHY Q2 



CHAPTER I. 
INTRODUCTORY. 

I. It is a little difficult to define the word "puzzle," especially to 
define it in such a way as to include all puzzles worthy of the name 
without at the same time making the definition so very wide that 
there remain no descriptive features, and consequently no real in- 
formation is conveyed. One authority 1 defines a puzzle as "a mechan- 
ical toy or other device involving some constructional problem, to 
be solved by the exercise of patience and ingenuity." A somewhat 
more inclusive definition is to the effect that a puzzle is "a thing 
difficult to understand or solve — especially something purposely ar- 
ranged so as to require time, patience and ingenuity to arrive at the 
solution of its intricacies." 2 Lindley 3 defines a puzzle as "a problem 
which is apart from the usual experience of the given individual either 
in subject matter or method." Of these two items the relatively more im- 
portant is method. Lindley further says : "Any problem which 
fulfills these conditions and which is tried chiefly for the sake of the 
reaction, and for the solution as such, may be a puzzle." 4 

For our present purposes we need to associate with the word "puzzle" 
at least the following characteristics: (a) a situation with a difficult 
and unknown solution, (b) a situation with an assuredly possible 
solution, (c) a situation all the factors of whose solution are en- 
tirely in the control of the one seeking to solve the problem presented 
thereby. The fact that a solution is possible has a certain stimulus effect 
upon the person endeavoring to solve the puzzle (this person we 
shall call the subject, or reagent). Knowing that the thing can cer- 
tainly be done he attacks the problem in a confident and expectant 
frame of mind which would not be regularly possible if he doubted 
the possibility of a solution. The unknown nature of the correct pro- 



(1) Bncyc. Brittanica. 

(2) Standard Dictionary. 

(3) A Study of Puzzles, Am. Jour. Psvch. VIII, 1S97. 

(4) ibid, p. 443. 



cedure in solving the puzzle makes room for the elements of time and 
ingenuity. The fact that all the factors of solution are to be completely 
in the control of the subject calls generally for small, easily handled 
mechanical or geometrical contrivances, and renders both the time taken 
in finding a solution and the procedure adopted for this purpose direct 
and valuable data representing the individual subject concerned. 

2. The many puzzles coming in a general way within these require- 
ments may be variously classified. They may be classified for instance 
(a), as to whether they involve motion in two dimensions (the Maltese 
cross puzzle 1 ) or in three (the twisled nail puzzle) ; (b) as to the number 
of correct moves necessary for the solution, after the proper starting ; 
position has been found, from one move (the horse-shoe puzzle) to 
eight (the key puzzle) or more; (c) as to what might be called their 
flexibility, i. e., while some puzzles require the relation of their various 
parts one to another to be changed (the nail puzzle), others permit 
no shifting of parts but only the direct removal of some parts leaving 
the other parts unmoved (the match puzzles), while still other puzzles 
are not to be moved in any part but something is to be done with the 
puzzle as a whole (the tracing puzzles) ; (d) as to the number of choices 
possible at each or any stage of the solution : in this respect the same 
puzzle may at different stages offer varying degrees of complexity (as 
in the second maze puzzle, where some stages offer but one choice out 
of two while other stages offer one out of four) ; (e) and then, puzzles 
may be further classified at length on the basis of the combination 
of any two or more of these four more fundamental features. Lindley," 
including under the word some puzzles which would not meet the con- 
ditions imposed above, has rather popularly divided puzzles into the 
following groups: (a) Language and word puzzles, including riddles, 
connundrums, charades, acrostics, etc. ; (b) mechanical puzzles, includ- 
ing some dependent on dexterity and perseverance, some dependent on 
a trick or secret, dissected and combination puzzles, physical puzzles 
which involve unique applications of well known physical laws, and 
other puzzles more complicated; (c) mathematical puzzles, including 
numerical, geometrical and unicursal or tracing puzzles. 

3. In using puzzles for the study of children and adults there are 
the following advantages, not all of them, however, unique: (a) This 



(1) These puzzle names refer to puzzles used in the second series of 
•iginal experiments herein reported. 

(2) A Study of Puzzles. Am. Jour. Psych. VIII, 1897. 



particular field is largely unworked. Outside the extensive research of 
Dr. Ruger 1 there is nothing yet printed which makes elaborate or de- 
tailed scientific use of the puzzle method for investigating the human 
mind, (h) The results of work on puzzles are such as lend themselves 
readily to exact record and tabulation, (c) Puzzles are sufficiently dif- 
ferent from the commonly accepted standards of intelligence, such as 
"book-learning" to furnish a new and independent set of investigating 
standards, (d) Puzzles such ag are used and described hereafter can 
be applied' to the young and old alike, (e) These puzzles demand for 
their solution some kind of motor reaction, (f) But this reaction rep- 
presents something far more complex than the reflex arc; it depends upon 
the functioning of a directly mental element, and this gives considerable 
purely psychic value to puzzle results. (g) Puzzles lie very largely 
outside the realm of daily or common experience, and their use is thus 
almost entirely free from the irrelevant factor of previous practice or 
familiarity. 

4. The methods used in studying puzzles or in studying the human 
mind through the use of puzzles should be varied. To confine an entire 
research to one single method, as Dr. Ruger does, is to invite incom- 
plete or unbalanced results. The best scientific method calls for the 
intensive study of a problem by what we might almost designate the 
extensive method. That is, the problem is to be attacked from all di- 
rections and investigated from a fairly comprehensive set of points of 
view. One method may give true results as far as they go ; but in the 
light of the results which would have been obtained from the other 
side of the problem, to to speak, when tested by a different method, 
these first results may be not only partial but non-representative. Few 
untruths are so deceptive as half-truths. What is perfectly true in its 
place, may, without itself being changed, become an untruth when con- 
sidered by itself with no reference to its normal relations. For such 
reasons a variety of methods should be used with the study of puzzles, 
and in the original investigations reported later herein several methods 
were used. The question as to which way found to be most economical 
and exact, consequently most scientific, will be discussed in its place. 

In using a variety of methods, however, there is the necessity of 
making all these fully comparable. If, for example, the auditory method 
and the visual method and the motor-experience method are all used, 
everything else should be the same — the same reagents, the same puzzles, 



(1) Archives of Psychology. No. 15, June 1910. 

7 



the same directions, the same formula of solution for each puzzle, and 
a general standardizing of all other conditions. This eliminates ir- 
relevant factors, greatly reduces the liability of errors creeping in, renders 
the consequent tables of data fully comparable, and in such ways con- 
duces most directly to scientific results. 

Results in the work with puzzles find their highest value in being 
truly representative results. This kind of results we should earnestly 
strive for — results which represent the human mind in general. No one 
cares particularly to know what kind of psychic equipment is possessed 
by a handful of individuals ; but if we have good reason to believe that 
the mental traits discovered in tlrs particular group of individuals hold 
true of men in general, then these individual records and the conclusions 
based on them immediately take on immense value : our particular re- 
sults rise to the significance of representative results. Now in order 
to obtain results of this wide-reaching significance attention must be 
given to the selection of reagents, to the selection of individual tests, 
and to the general methods of the entire procedure. Enough has already 
been said, at this point, about such methods as lead to fully comparable 
results. As to tests, there should be several of them, all different, yet 
all proceeding on the same general principle. The differences in these 
tests should be governed by the principle of representative value, which 
will result in the entire series of tests covering all the chief lines of ap- 
proach to the mental powers under investigation. If the work is to be 
chiefly extensive the group of reagents should be large and homogeneous ; 
if the work is to be chiefly intensive the reagent group need not be so 
large but may well be made up of members varying between themselves 
as much as possible. By observing such guiding principles as these the 
results obtained will be increasingly representative, which means they 
will be possessed of increasingly general value. 

5. This present investigation is undertaken in the belief that puzzles 
provide a relatively unknown but a very promising means of studying 
certain phases of the human intelligence. The investigation has been 
pursued in the further belief that the observance of such principles as 
have been briefly outlined above will lead to scientific and fundamentally 
valuable results. 

After a historical and critical review of work already done in this 
field, two series of puzzle tests are presented. The first series, which 
is somewhat preliminary, deals with the problem of the correlation be- 
tween puzzle learning and school intelligence. The second series is an 



intensive study by means of puzzles of a small but carefully selected 
group of subjects, with special attention to individual differences and 
methods of learning. 



CHAPTER II. 
HISTORICAL AND CRITICAL. 

i. GENERAL. 

There is exceedingly little to be said in a general historical survey of 
the use of puzzles as mental tests. And this for the good reason that 
puzzles have not been used to any considerable extent for this purpose. 
Outside the early but quite general discussion of Lindley and the later 
and careful research of Ruger, both to be noted below, we have nothing 
more than very brief references, in a few books on mental tests, to the 
possibility of using puzzles for this purpose. Chronologically Lindley 
antedates all others, but it may be well to glance at a few scattered 
references before noting Lindley more particularly. 

In the Binet-Simon tests, which first appeared in full in L'annee 
Psychologique in 1905, there are at least two tests closely approximat- 
ing if not including the puzzle situation. In test No. V for 5 year olds 
the child is so to place two separated right angle triangles as to form 
a square like the one shown him at the same time. 1 Again, in the 
second test for adults the two parts of a calling card cut diagonally are 
to be mentally pictured in an unusual given position. 2 These two tests 
remind us of the geometrical puzzles described hereafter. 

Partridge barely refers to the possible use of puzzles as tests but 
gives no particulars. 3 

In his volume on Educational Psychology Thorndike places a figure 
looking like a maze puzzle. 4 This is but a single crooked path r however, 



(1) A Method of Measuring the Development of young children. Trans, by 
C. H. Towne, 1912, p. 24. 

(2) ibid, p. 60. 

(3) An Outline of Individual Study, 1910, p. 191. 

(4) Educational Psychology, 1910, p. 240. 

10 



within the two side lines of which the subject is to trace with a pencil 
a line of his own. The test here has no direct relation to the puzzle 
consciousness, but centers on steadiness of muscular control. The ir- 
regularity of the figure, however, suggests a maze puzzle, and may be 
taken as a harbinger of such. 

Several writers speak of the value of the ink-spot test — among them 
Plye. 1 The perceptual interpretation of these ink spots approaches 
certain types of puzzles ; but this is as much as can be said. 

Breitwieser refers to puzzle pictures but gives no details. 2 The method 
he recommends calls for a time record of how long it first takes the 
subject to recognize the hidden forms in the pictures, and for a further 
record of the time it takes to recognize these forms again after a space of 
5 or 10 minutes. 

We find a bare mention of the jig-saw and other puzzles in Groszmann, 
for the purpose of testing judgment in the intermediate period. To this 
is added a reference to geometrical puzzles for the purpose of testing 
judgment in the advanced period. 3 

The form board approaches the puzzle idea. This test is mentioned 
by several, including Whipple. 4 The first use of the form board as test- 
ing device is credited to Naomi Norsworthy, 5 and this particular piece of 
apparatus has recently been made the subject of an extended monograph 
by Sylvester. 6 The form board, however, can hardly be classified as a 
regular puzzle although it strongly suggests the puzzle form. 

An advance is registered by Healy and Fernald in their use of the com- 
bination form boards and picture puzzles, and of both round and square 
construction puzzles. 7 These latter are true puzzles, but are limited 
in that they are all built on the conception of form. These investigators 



(1) The Examination of School Children, 1913, p. 33. 

(2) Psychological Experiments, 1914, p. 113. 

(3) The Study of Individual Children, 1912, pp. 60, 64. 

(4) Manual of Mental and Physical Tests: Simpler Processes, 1914, p. 299. 

(5) The Psych, of Mentally Defective Children, Archives Psych. No. 1, 1906, 
pp. 25, 26. 

(6) The Form Board Test. Psych. Monographs Vol. XV, No. 4, 1913. 

(7) Tests for Practical Mental Classification. Psych. Monographs Vol. XIII, 
No. 2., 1911, pp. 11, 13, 14, 16. 

II 



made use of the puzzle box in testing children, 1 as Thorndike did in test- 
ing animals." The puzzle box used with children by Healy and Fernald 
could be opened only by a definite sequence of 5 or 6 steps. Here, of 
course, we again have a true puzzle. 

Without question the most suggestive work involving puzzles before 
the appearance of Ruger's monograph is that given at length by E. H. 
Lindley. 3 After an effort to define a puzzle and to classify puzzles 
(referred to above) Lindley reports the results from a rather elaborate 
questionnaire to which 556 replies had been received. By this method 
Lindley had sought information about the puzzle interest in children 
and adults. He concludes that there is in human nature "instinctive sub- 
strata of puzzle interest." The persons replying to the questionnaire 
revealed greatest interest in language and word puzzles, next in mechan- 
ical puzzles, and least interest in arithmetical puzzles. This order- 
of interest changes, Lindley concludes, with age, the more complex 
gradually driving the more simple puzzles from first place in interest. 4 
Lindley exhibits his results by several tables and curves, and expresses 
himself as impressed' by the "persistence and tenacity with which a 
puzzle bids for attention and holds it." 

In addition to the questionnaire, Lindley put through a fairly ex- 
tensive experimental test. Using a unicursive or tracing puzzle of 
moderate difficulty he tested 500 school children and 300 adults. He 
found, among other things, that the average number of trials necessary 
in order to succeed did not vary greatly with the varying ages of the 
school children, 5 although there was an observable, tendency in the older 
children to analyze the situation and profit by errors. The objective 
record of the adults was supplemented by an introspective report. 
Lindley concluded that adults stud}'- the figure before proceeding as 
children do not. He attempted a gradation of methods of solving his 
puzzle, and adopted a threefold grouping. The children, he said, used 
almost entirely the sense-trial and error method, as animals. The most 
thoughtful adults, on the other hand, used what Lindley calls the con- 



(1) Ibid, p. IS. 

(2) Animal Intelligence, 1911. 

(3) A Study of Puzzles with special reference to the Psychology of Mental 
Adaptation. Am. Jour. Psych. VIII, 189' 7. 

(4) Ibid, p. 446; 453. 

(5) Ibid, p. 463. 

12 



ceptual method, 1 — that is, a deliberate search for underlying principles, 
with an attempt at analysis. Between these two extremes many used 
what Lindley calls the perceptual method : this is somewhat of a mixture 
of the other two, being an advance upon the sense-trial and error 
method but not making use of reason as in the conceptual method and 
attaining only a hazy idea of the relation. 

All told, Lindley's work deserves much praise. It broke the path 
for other investigations in an unworked but very promising field. Ruger 
acknowledges his indebtedness to Lindley, and evidence of the first 
writer's influence abound in the later investigator's monograph. To a care- 
ful consideration of this piece of painstaking research we now turn. 



2. EXAMINATION OF DR. RUGER'S MONOGRAPH. 

The only serious attempt to work out the psychology of the puzzle 
is that recorded by Dr. H. A. Ruger in his monograph entitled "The 
Psychology of Sufficiency," 2 and to this we must give some attention. 

A. Objective Report. 

Dr. Ruger's aim in his investigation is to show by the use of puzzles 
how the human mind meets and masters a new situation. This general 
aim includes the testing of such mental powers as "the ability to size 
up a -situation, to eliminate the irrelevant, and to use independent judg- 
ment in that selection." It also covers the investigation of "the great 
role played by more or less explicitly conscious assumptions as to the 
nature of the problem" facing the subject in puzzle form. 3 

His problem he sketches somewhat as follows : "The present study is 
an attempt, under simplified conditions and with special emphasis upon 
the motor type of process, to analyze human methods of meeting relatively 
novel situations and of reducing their control to acts of skill. It differs 
from previous studies in the learning process "in that the original situa- 
tion is distinctly of the problem type, and in that the acquisition of skill 
in the succeeding manipulations also involves the problem type of 



(1) Ibid, p. 471. 

(2) Archives of Psychology. No. 15, June 1910. 

(3) p. 4. 

13 



consciousness to a very considerable degree . . . the interest in the 
present study is dynamic rather than structural. It deals with the part 
which different sorts of thought processes actually play in the meet- 
ing of novel situations, and, as far as possible, with the conditions 
favoring the development of variations. The problem as thus treated 
may have lost somewhat in precision on account of the breadth of pro- 
cesses entailed, but it is hoped that there has been a corresponding gain 
in continuity and in the exhibition of organic relationships." 1 

Ruger's method consisted in experimental work with twenty-seven 
subjects on a number of different puzzles, thirty-seven in all. Records 
were kept of the time taken to solve each puzzle at each separate trial, 
of the subject's oral or written introspective account as to how he 
solved the puzzle, of the experimenter's observation of the number 
and kind of moves made by the subject while working on each puzzle, 
and of all exclamations made by the subject during the course of each 
trial. These various records are presented in the form of tables, charts 
and graphs, and in the latter portion of the monograph many of their 
features are discussed somewhat in detail. Of the twenty-seven subjects 
thirteen were graduate students, seven had professional training in 
psychology, two were instructors in related fields, one was the laboratory 
mechanician and four were grammar and high school boys. All but the 
latter five had some special interest in psychology. Five of these in- 
terested subjects were women. 2 

The procedure in these experiments is designated as "very simple." 
"The subject was seated comfortably at a table, on which the puzzle 
was placed. The puzzle was covered by a screen. After the warning 
signal, a starting signal was given, and the screen removed. When the 
manipulation for the given trial had been completed, the puzzle was im- 
mediately removed by the operator and prepared for the following trial. 
The subject was given no opportunity to examine the puzzle except 
during the actual trial. The number of trials for a given subject with a 
given puzzle varied from i to 1440. The standard number was 50 ... . 
The number of trials at a given sitting varied with the subject and the 
puzzle. The sittings were usually of an hour and a half in length. In 
some cases an entire series of 50 trials was completed in this interval. 
In others several periods were consumed in gaining the first solution." 3 



(1) pp. 1, 2. 

(2) p. 6. 

(3) p. 3. 



14 



Most of the records are for one-way solutions, the puzzles being put 
together again out of sight of the subject. The instructions to subjects 
were very brief and general. In most cases the subjects were told no more 
than that some part of the puzzle was to be removed. They were, how- 
ever, asked to solve the puzzles as rapidly as possible. As a general 
rule a subject continued working on a given puzzle until complete skill 
was attained in its solution. Dr. Ruger's results are gathered under 
five heads, viz., Methods of Learning, Conditions of Efficiency, Transfer, 
Memory and Plateaus. 

(i) In summing up those results of his work which bear on methods 
of learning Dr. Ruger places chief emphasis on the discovery that there 
is no such clean-cut distinction between what have been called "animal" 
and "human" methods of learning. By the animal method has generally 
been meant the "trial and success" method in which success has been 
achieved by the mechanical stamping in of random or instinctively de- 
termined movements. The human method, on the other hand, has 
been described as one of "reasoning"— an understanding of the principles 
involved which results in learning by a single successful experience. To 
this Dr. Ruger replies that he finds frequent cases of the "trial and 
success" method well along in the course of a given subject's experi- 
ments with a given puzzle. There are various points of resemblance 
between the methods of these human reagents and the methods sup- 
posed by many to be confined to animals. These two methods, there- 
fore, do not come near exhausting the different forms of learning, but 
are best considered "as limiting members of a series of methods in 
which different types of analysis play an important if not a determining 
role." 1 

(2) The conditions of efficiency center on the rise of variations in 
the methods of detailed procedure. Ruger finds, as others before him, 
that a sudden drop in the curve of learning follows a variation of 
method. Most of these variations first came unpremeditatively, but suc- 
cess then depended upon "the extent to which they were treated as 
hypotheses to be systematically tested with subsequent adoption or re- 
jection." 2 Physical condition was found to influence the occurrence of 
variations. Likewise attitude. Here Ruger points out that those reagents 



(1) P. 8. 

(2) p. 15. 



IS 



who were embarrassed by the presence of the observer, who "knew the an- 
swer," and those who were laboring under the notion that their self was 
being tested, were so self-conscious that, instead of centering attention 
on the puzzle, it was centered on themselves, with a consequent loss 
of successful variations of method. Moreover, variations were inhibited 
by false assumptions as to the method of solving a puzzle. The most 
successful way of breaking up these fixed assumptions was to analyze 
them out, criticize them, and then to reject them in search of new points 
of view. The shifting of assumptions, whether occurring by accident 
or purpose, often resulted directly in the solution." 1 Ruger concludes 
here that "efficiency was found to be directly dependent upon success 
in getting the most appropriate method or technique." 2 

(3) Dr. Ruger uses the term "transfer" in a broad sense, including 
the general as well as the specific effects of an experience on subsequent 
experience. He found that "the value of specific habits under a change 
of conditions depended directly on the presence of a general idea which 
would serve for their control." 3 This general idea depended in turn upon 
precision of analysis. Often when two experiences had objective ele- 
ments in common there was no beneficial transfer because this similarity 
failed to be recognized. It was especially noted that previous mathemat- 
ical training exercised no observable effect on the dynamic constructive- 
ness called for by the puzzles. The greatest transfer was between simi- 
lar puzzles. Yet even here, an act of analysis was necessary in addition 
to the vivid image of the related puzzle. 4 

(4) Memory was found to sustain a striking relation to continued 
analysis. In most instances "memory cues were promptly substituted 
for continued perception of relations." 5 If these memory cues were cor- 
rect much time was saved, but if, as frequently happened, the cues 
were erroneous much confusion resulted — the subject sometimes being 
in this way held for an indefinite period on the wrong line of procedure. 
The best success came to those subjects "who held their memories flexibly 
as hypotheses subject to rejection or revision as the case might be." fl 



(1) p. 18. 

(2) p. 14. 

(3) p. 19. 

(4) p. 20. 

(5) p. 87. 

(6) p. 20. 



16 



(5) As to plateaus, the experiments confirmed the generally accepted 
opinion that these are stages of stagnation due to the non-appearance of 
variations. Ruger finds plateaus due to several somewhat similar causes : 

(a) where there is a shifting back and forth between rival methods, 

(b) where "some feature remained intractable to control," or (c) where 
a method not efficient was nevertheless clung to. To get off a plateau 
a variation in method was necessary accompanied by its conscious use 
as an hypothesis. 

(6) In a later section of his monograph Dr. Ruger discusses results 
bearing on "Puzzle Material and Tests of Intelligence." He found th* 
ratio between the first and second working of puzzles by his subjects to 
average 7:1. Similar ratios for monkeys had been found to be 2:i, 3 
and for raccoons 3 :2. 2 After discussing various possible methods 
of comparing intelligence, each of them subject to rather serious 
objections, he concludes that members of a group working with 
a single puzzle might be compared if the following factors could 
be either equated or controlled, viz., physical condition, degree of de- 
velopment of the fundamental function, concrete related knowledge, 
general methods, and mental attitudes. To Dr. Ruger one of the best 
ways of making such a comparison would be to train the subjects with a 
puzzle of a certain type and then to make a study of their ability to use 
this training in dealing with "a more or less thoroughgoing transforma- 
tion of the principle involved." 3 

Dr. Ruger' s conclusions can probably be briefly stated in two divisions. 
The first has to do with the obtaining of efficiency. He gives it as his 
view that "the course of efficiency in the practice curve is largely a mat- 
ter of securing the appropriate variations and their conscious control." 4 
He finds that "the drops in the curve depended. very largely on variations 
in method and their conscious use as hypotheses." 5 The rise of these 
needful variations was favored by such factors as a high attention level 
and the problem-attitude rather than the self-conscious attitude ; and the 
use of these variations as conscious hypotheses was obtained by a full 
control of all assumptions, which led to the constant trying out of all 
suggested steps of procedure and the continual search for new points 



(1) Comp. Neur. and Psvch. Vol. XVII, p. 211, L. W. Cole. 

(2) Am. Jour Psvch. Vol. XIII. pp. 126, 127, A. J. Kinnaman. 

(3) p. 47. 

(4) p. 86. 

(5) p. 20. 

17 



of view. The obtaining of skill was greatly facilitated by analysis, under 
which word Ruger includes the preeminently important power of getting 
"some mental grasp of the process as a unity." 1 The second division 
of Dr. Ruger's conclusions is related to subjective methods of learning 
and is to the effect that no one method of mental process predominates, 
nor can the processes of the problem-consciousness be reduced to two 
general methods, "trial and success" and "reasoning," but wide and at 
present irreducible variety characterizes the methods of mind by which 
different persons attack novel situations. 

B. Subjective Report. 

In discussing the quality and value of the work of Dr. Ruger it must 
first be said that if the form of his report had been somewhat different 
greater clearness might have resulted. For instance, his general con- 
clusions are difficult to locate. While the last chapter, that on Transfer, 
heads its final section as "General Discussion and Summary" a reading 
of this passage shows that almost the entire subject matter has to do 
with Transfer, which is only one of his several groups of results. One 
searches in vain for a succinct but comprehensive statement of general 
conclusions on the work as a whole. The nearest approach is Chapter II, 
General Statement of Results, but this is too lengthy for a statement 
of conclusions, besides it makes prominent several topics (Methods of 
Learning, Memory, Plateaus) which are either slighted in the general 
body of the book or are passed over in all but complete silence, and, 
further, it contains no reference to a topic to which he later devotes the 
whole of one of the six chapters of the book, viz., Tests of Intelligence. 
To mention these things, is, of course, but formal criticism ; nevertheless 
it represents a genuine reaction to the structure of the monograph as a 
whole. Can it be that the author in this particular case expects the 
reader to attack the monograph as a "novel situation" calling for the 
vigorous use of the reader's "problem-consciousness"? 

When, on the other hand, we take into consideration the amount of 
work done in obtaining data for the monograph there is abundant ground 
for admiration. The author speaks of 7000 different cases, and the 
records show that at least a few of these cases ran into the thousands 
of seconds and called for repeated sittings. All this represents an im- 
mense amount of energy concentrated on one very limited line of pro- 



CD p. 20. 

18 



cedure. Our only disappointment arises from the paucity of definite 
conclusions out of such an overwhelming amount of labor. 

Dr. Ruger's general method and procedure seem open to question 
at a number of points. As to the number of subjects used and their 
respective participation in the investigation, several things need to be 
pointed out. From twenty-seven subjects one can unquestionably discover 
much concerning the workings of the human mind if the work of these 
subjects is quite comparable. But there is no sufficient ground to be- 
lieve that this important condition was obtained in the investigation be- 
fore us. If this criticism is in error it is due in large part to the 
failure of Dr. Ruger to give anywhere a complete statement of just 
how many puzzles and what particular puzzles each subject worked with. 
Nor does he anywhere give complete tables of results. His discussion 
abounds with facts and figures, but we are given to understand that 
all these are selected. In many tables only a very few of the twenty-seven 
subjects have their records given, and in no table are more than nine 
of the entire twenty-seven shown at once. Moreover, none of the larger 
tables gives comparative records with an equal number of trials in each. 
Some of the subjects may show say fifty trials, others only half as 
many or less than half. Further indications are not wanting to sug- 
gest the partial incomparableness of these records. For instance, from 
some subjects the observer screened himself, but not from all. This 
necessarily affected both the subject's personal attitude and the experi- 
mentor's facility for observing. Moreover we are told that "in some 
cases the shift of assumptions was due to instructions given by the 
operator to the subject to critically define the assumption under which 
he was working, to seek out other assumptions, and to test them either 
in turn or in accordance with their probability." 1 Why was this ex- 
tremely valuable instruction given to some subjects at a critical moment 
but not to all? It surely produced decided differences in results. For 
such reasons as these we are unable to accept the records of the twenty- 
seven subjects as comparable. They did not all do the same puzzles, nor 
sit through an equal number of trials, nor were they all subjected 
to the same procedure. 

This being the case there seems to be good grounds for questioning the 
general representative value of the results outlined in the monograph 
under discussion. Twenty-seven reagents with records seriously incom- 



(1) p. IS. 

19 



parable can hardly furnish sufficient basis for results standing as rep- 
resentative of the human mind in general. This very point seems to 
be implicit in many of the author's statements. With commendable care- 
fulness he hesitates to make very definite statements, but tells us that 
such and such is "generally the case," "frequently found," holds "for the 
most part," and is "chiefly the explanation," etc. Such conclusions may 
truly help us on our way, but they disappoint our expectations from 
such a laborious and detailed investigation. In one sense the best sup- 
ported conclusion of all seems to be that which declares that the mental 
processes under investigation appear to be extremely varied. This is 
surely the direction in which the definite data the author has chosen to 
give us point. Might it not be, however, that even this conclusion does 
not represent the actual facts of the case? Would not a more repre- 
sentative or, on the other hand, a more homogeneous group of reagents, 
handled in such a way as to make all their records thoroughly comparable, 
have put us on the trail of some underlying mental unity in the problem- 
consciousness, or at least have brought us up to a few great types of 
problem-functioning? Such seems most reasonable to suppose. Such 
kind of a study would be greatly facilitated by a series of preliminary 
cests to free the problem from excrescences and to block out the main 
line of work. The results of such a study would be most admirably made 
secure by a careful set of control-experiments. The possibilities of valua- 
ble discovery from such a study would, moreover, be decidedly increased 
if, instead of having all the work done by one method, such as the no- 
instruction procedure by which alone all of Dr. Ruger's subjects worked, 
there should be given a careful selection of differing methods, all other 
circumstances involved being rigidly kept the same. 

As to Dr. Ruger's plan of keeping a record of false moves it is ex- 
tremely improbable that it amounted to anything definite. With some 
very simple puzzle forms a correct record of this nature might be kept, 
but it seems practically impossible to record all false moves when the 
puzzles are complex and when many of them are in three dimensions. 
This matter is dealt with in the report of original investigations found 
later in this book. It may be sufficient here to say that to know by 
watching what are truly false moves, to know when to count a partial 
move false, to know when to make allowance for moves inhibited al- 
most as soon as begun, to know how to divide up a series of connected 
motions into a definite number of moves, to know just when to count 
a move false which, if having other antecedents would not be false, to 



be able to act promptly and unerringly along all these and similar 
lines, and then to be able to keep an accurate record and for all sub- 
jects a full and complete record of such observations, giving the same 
value to the same form of move among all subjects alike, this is surely 
expecting the impossible. If, on the other hand, the record of moves 
is not kept as carefully and fully as here suggested it becomes merely 
a jotting of selected and partial observations and has no substantial 
scientific value. Here again Dr. Ruger seems implicitly to deny the 
value of his own method, for in discussing the experiments he almost 
never makes any reference to this record of false moves. 

Another item is the record of remarks or exclamations made by the 
subject in the course of his work on a puzzle. There is no doubt that 
occasionally a gleam of light may come to the observer through such 
remarks, that, is, if they are made. Here we are dealing with a matter in 
which personal differences function most directly. Some persons will 
work long in absolute silence, others will be saying things most of the 
time. This feature of course makes such a set of records entirely in- 
comparable. It we overlook this objection and take the record of each 
separate subject as quite complete in itself, it is extremely question- 
able whether few remarks made by a subject will convey any informa- 
tion, not immediately obtainable also from an observation of his move- 
ments made in handling the puzzle. For instance, when we see a 
subject with sudden eagerness make two or three swift, correct moves 
which solve the puzzle, we do not gain any information by hearing him 
exclaim at the beginning of this spurt, "Ah, now I have it!" We 
could tell that from h's face, from the swiftness and directness of his 
moves and from his immediate success. In short it is exceedingly ques- 
tionable if the explanations from those few subjects who made them re- 
veal anything more than states of mind — not mental processes. But 
it is processes we desire to study, and, furthermore, the states of mind 
are about as fully disclosed in other ways. 

Along with the two foregoing records Dr. Ruger used as a basis of 
his discussion a written record of each subject's introspective report of 
his mental activities in solving the puzzle. This was either written 
by the subject himself at the conclusion of the sitting or was dictated 
by him. This record ought to prove the most valuable of the three. 
It is not, however, free from serious objections. If in order to obtain 
a full record the observer urged the subject to watch his own mental 
activities and report thereon in detail either during the course of the 

21 



sitting or at its close, this could not fail to divide the attention of the 
subject. What time and energy he spent in trying to catch his mental 
processes was just so much attention taken from the puzzle. This of 
course would affect his solution of the puzzle. In tead of having an un- 
broken puzzle-consciousness, upon the need of which Dr. Ruger rightly 
lays much emphasis, the reagent would alternate with his puzzle-conscious- 
ness an introspective-consciousness or a report-consciousness. This would 
seriously interfere with the mental attack on the puzzle, the nature 
of which mental attack the experiments were aimed to disclose. On the 
other hand, if nothing was said to the subject about a forthcoming in- 
trospective report but he was allowed to lose himself completely in the 
problem of the puzzle in his hand (which is without doubt the better way), 
then how complete or correct an introspective account can we look for 
when it is unexpectedly called for at the close of the sitting? As is 
generally acknowledged, the so-called introspective report would be noth- 
ing more than a memory report. If the process of solving the puzzle 
had been long, being made up of an immense variety of moves, 
hypotheses and trials, some correct, some false, could we expect the sub- 
ject to remember enough of all this process to make his report any- 
thing like complete or even comprehensive? Assuredly not. Pure in- 
trospection is a self-contradictory notion. Memory of mental states and 
experiences is likely to be weak and incomplete in direct proportion to 
the degree to which the object of attention with which these particular 
states and experiences are associated is objective. Now few things could 
be more objective than a concrete puzzle, made of wire or wood, held 
in one's fingers, and to be taken apart by the fingers. To the degree to 
which the subject gave his genMm^ and undivided attention to attacking 
the puzzle, which was what h#^as desired to do, to that degree was 
he rendered incapable of giving a correct or complete introspective re- 
port. In other words these two parts of the method are mutually de- 
structive: if the subject gives that kind of attention to his puzzle which 
is necessary in order to make his attack upon it of any scientific value, 
he loses his grip on his inner processes and cannot report them satisfac- 
torily; if, on the other hand, the subject is able to give a full and de- 
tailed introspective report it shows that he was watching his subjective 
conditions instead of attacking the puzzle, and consequently his report 
has no value as a record of the puzzle-consciousness. 

We may wonder if once more the author of the monograph does not 
give implicit recognition of the reduced value of his own methods — 

22 



this time as to the introspective records. For at several important points 
in his discussion he abandons the introspections of his subjects and with 
a sense of decidedly greater certainty he records his own introspections. 
For instance, we read : "As stated above, the writer finds the process of 
analysis, so far as his introspections have gone, to be of the same sort 
whether occurring in the field of perception or of imagery. He found 
great difficulty in the attempt to image tridimensional transformations in 
advance of any movement, but, on the other hand, he found at certain 
stages a decided help in withdrawing the puzzle from sight or in clos- 
ing his eyes and then attempting to work out the relations involved." 1 
Again we read : "These suggestions are based directly on the writer's 
introspections, but are supported by occasional remarks of subjects to 
the effect that they seemed to see the relations involved in solution 
directly, and without the use of imagery." 2 Here we have the studied 
introspections of the author given — one who was not a subject, one who 
could not very perfectly bring himself to the puzzle-consciousness which 
the monograph studies because he knew how to solve the puzzles and 
was therefore unable to attack them as were those to whom they were 
puzzles indeed. This does not mean that Dr. Ruger's own introspections 
have no value, nor that they are entirely out of place in a discussion of the 
work of other subjects, but the injection of his own introspections makes 
easier, to say the least, the suggestion that he realized to a certain 
degree the inadequateness of the introspective reports of his subjects. 
These reports from subjects are by no means to be disregarded. Many 
of them are suggestive and some of them enlightening. Yet the value 
of all introspection must be assigned in full light of the above remarks 
upon the difficulty of obtaining such records anywhere near complete, 
comprehensive or representative. If introspection is ever to be given a 
high value it is under circumstances when the mental condition can be 
caught on the wing, so to speak, when, by a sudden change of attention- 
focus, the mind can catch a glimpse of the fleeting form of its ante- 
cedent state. Of course even this after all is but memory, but it is ex- 
ceedingly recent and fresh and is therefore likely to be vivid and correct. 
This practice requires some experience and skill. Now it is obvious that 
when one is pondering hard over a puzzle he cannot swing his attention 
suddenly upon himself every few seconds. This would fatally interfere 
with the normal process of attacking and solving the puzzle. While 



(1) p. 35. 

(2) p. 13. 



23 



it may be granted, then, that under certain especially favorable conditions 
introspection may yield highly valuable results, it ought to be acknowl- 
edged that these favorable conditions are emphatically precluded by all 
genuine states of puzzle-consciousness. This criticism of introspection 
deals of course only with free or uncontrolled introspection, for this is 
the kind of which Dr. Ruger endeavors to make use. 

In his outline of method Dr. Ruger places almost all his emphasis up- 
on the results to be obtained from the three records above discussed. 
His practice, however, seems better than his theory, and we find 
throughout the book many tables and graphs based entirely on another 
factor, viz., the time-element. In giving such a large place to records of 
time in his discussion the author may tacitly be admitting the final 
insufficiency and unsatisfactoriness of his records of exclamations, moves 
and introspections. As a matter of fact the time record of these 
twenty-seven subjects appears to be the only record of their puzzle- 
working which is equally applicable to all, which is objective and there- 
fore complete, and which, at the same time, is to the last detail com- 
olete. It is wise therefore to make this record the basis of considerable 
discussion. In fact it is doubtful if very exact knowledge of the pro- 
cesses of the mind can be obtained by any form of subjective record. 
The very purpose of puzzle tests is to seek for satisfactory objective 
tests and evidences of subjective conditions. 

The chief value arising from the introspective reports in this mono- 
graph is to provide an explanation in mental terms of a successful work- 
ins: of the puzzle. This use of the introspective method is valuable in 
Dr. Ruger's work, providing we are ready to take the risk of accepting 
as reasonably complete and correct the subjective reports made by the 
reagents at the conclusion of each sitting. Dr. Ruger's numerous quota- 
tions from these reports seem to justify one of his main conclusions, 
namely, that efficiency arises in connection with the adoption of new as- 
sumptions and their use as working hypotheses. Another valuable and 
well substantiated point is that having to do with the distributing effect 
of the self-consciousness rather than the problem-consciousness. This 
result was reached through observation on the part of the experimentor, 
compared with the time records, and has nothing to do with introspection. 

There remains what is in some respects the most fundamental ques- 
tion of all. It has to do with the author's aim. As previously stated, 
these experiments were devised and put through with the purpose of dis- 
covering how the human mind attacks and masters a novel situation. 

24 



From this we understand that Dr. Ruger uses puzzles as representing 
novel situations in general, of all sorts and particular conditions, just 
so long as they are novel and must be attacked by the human mind. 
Now the question arises, is this a safe assumption? In other words 
does the method, in this case, agree with the aim? 

Before one can accept this general representative value of mechanical 
puzzles he must first clear up several perplexing phases of the situation. 
For instance, while puzzles unquestionably present novel situations, these 
are artificial situations, and are from the first recognized as such. How 
close does this come to the novel situations of ordinary life, which are 
never artificial? Again, puzzles admit for the most part of only one 
way of solution, while to many of the problematic situations of life there 
is more than one way out. Does this feature affect the representative 
value of the method? Further, with puzzles one is dealing with dead 
matter, which is ever the same, which will not yield nor change its 
form. But in the novel situations of life one almost always finds 
other human personalities as part of the factors of his problem, and these 
factors need to be handled in quite a different way from unresponsive, 
unyielding material things. The right kind of dealing with the personal 
factors opposing a given individual's freedom will result in their dis- 
appearing as parts of his problem, but the wrong way of dealing with 
such personal factors will only increase the seriousness of their opposi- 
tion and thereby render the individual's problem all the more complex. 
There is nothing in mental puzzles which presents such a delicate prob- 
lem as this. Again, when one handles a puzzle his problem is to change 
the puzzle to fit him, the person ; but when one meets a novel situation 
m life it is quite frequently a situation of such proportions that he can- 
not alter it materially but must on the other hand change himself to fit 
the situation, and by thus doing he solves his problem. And onc e more, 
the subject knows in advance that to every puzzle placed in his hands 
there is a complete solution, and he knows that the experimentor is 
fully acquainted w : th this solution. But many of the novel situations in 
life cannot be faced or attacked with such certainty. We often question 
whether there is any satisfactory solution to many of them ; rather they 
threaten to crush us, and we attack them in quite a different frame of 
mind than that with which we sit down to work out a harmless puzzle 
which a friend has already solved before us. Does not this affect the 
mental processes involved? 

Now, before one can accept what seems to be Dr. Ruger's underlying 

25 



assumption in this puzzle test the above questions must at least be taken 
into careful consideration. There is, to be sure, the element of novelty 
common to both the puzzle and the problem-situation in general life. This 
is quite fundamental to both, psychologically speaking, and is good as 
far as it goes. But in the light of such considerations as those just 
outlined, and of other similar ones that might be urged, there is difficulty 
in finding oneself ready to agree to the proposition that the way the 
human mind attacks a mechanical puzzle is representative of the way it 
meets and masters any life situation which is conceived as presenting 
some sort of problem. 

If this objection to Dr. Ruger's assumption were found to be well 
grounded it would not follow by any means that the value of his mono- 
graph was therebv destroyed. There still remains suggestive results, 
quite probably true. The damage wrought by the self-consciousness, the 
great gain resulting from a deliberate analysis of a novel situation, the 
advantage of being able to see a complex situation as a unity, the in- 
creased probability of a successful solving in proportion to the rise of 
the attention-level, and the widespread variety of mental activities 
among individuals —these and other results previously indicated give 
positive worth to the monograph and help make it a valuable piece of what 
after all must be called pioneer work in this promising field of investi- 
gating the actual processes of human intelligence. 



26 



CHAPTER III. 

First Experimental Series. 

THE CORRELATION BETWEEN PUZZLE 
LEARNING 
and 
SCHOOL INTELLIGENCE. 

i. INTRODUCTORY STATEMENT. 

As stated in the General Introduction, the purpose of this investigation 
is not to study intelligence in general, nor even a test of intelligence in 
general. Our problem lies in the field of the tests of intelligence, but is 
narrowed down to the one particular inquiry, viz., is there any determin- 
able correlation between what is called school intelligence in children, and 
their ability to solve simple mechanical puzzles ? All other purposes have 
been disregarded and every effort has been centered on this one definite 
point. 

The term "Mechanical Puzzles" is used to distinguish the puzzles ex- 
perimented with from mathematical puzzles, verbal puzzles, or various 
other forms, of which there are many. The puzzles here used belong 
to the class of simpler mechanical puzzles, chosen thus for the reasons 
given below. 

In view of the preceding historical and critical section, it may be well 
at the outset of this report of new work to indicate in brief form a 
number of the particulars in which the present investigation has sought 
to avoid errors or weaknesses appearing in previous work of the same 
nature and has endeavored to make the results herein recorded safe and 

27 



sure. Let it be said, then, that the present investigation has aimed at cer- 
tainty and value in the following ways, among others : 

(i) There has been no changing of experimentors during any series; 
all the tests in a series being given by the same experimentor. 

(2) All the tests have been applied individually, and not to children 
in groups or roomfuls. 

(3) All the tests have been given in private. 

(4) During the course of every test the experimentor has allowed 
himself to be taken up with no other matter which would in any degree 
distract his watchful attention from the reagent. 

(5) Even the room in which the tests have been given has been 
stripped as bare as possible of all possible sources of distraction. 

(6) Every test has been given to all students in precisely the same 
manner, down even to the directions given for working the test. 

(7) The children have all been of the same social status. 

(8) The children have all been students in the same school. 

(9) The children have been students in this school at the same 
time and were tested at the same time. 

(10) All features of sex and age have been carefully worked out 
as will appear below. 

(11) Both Spearman and Burt make something of the value of zeal 
in connection with such experiments. In the tests herein recorded, the 
zeal was good throughout. The students tested were, among other 
things, given exemption from a decidedly unpopular Study Hall. The 
students tested were, moreover, permitted, within certain limits, to 
choose their own time of day for taking the test and obtaining this ex- 
emption. In such ways as the above the reagents were all as nearly 
alike as possible, except in the factors investigated. 

(12) Tests given were all new, never being used before by others 
in this way. 

(13) The tests were few, four in number, and were all of the same 
nature. 

(14) The apparatus was simple and uncomplicated, attracting no at- 
tention to itself. 

(15) No previous practice was given in any instance, thus excluding 
this feature which often introduces personal differences that would 
not otherwise function in this kind of experiments. 

(16) Very careful mathematical procedure has been observed through- 



28 






out, not only are all results worked down to a definite figure by the most 
approved methods, but in every case mean variation or probable error 
has been given. 

(17) While the tests have involved of necessity sensori-motor ele- 
ments, they have been of such nature as to place the emphasis upon 
the purely intellectual factors involved. This will appear more particular- 
ly in the detailed descriptions which follow. 



2. REAGENTS. 

The tests herein described were made on students. These naturally 
fall, by reason of differences in age and mental maturity, into several 
large groups. 

Group I, the smallest group, consisted of nine adults (five men and 
four women), all near thirty years of age and all engaged in advanced 
study of one kind or another. Very little use was made of this group, 
but it was of service in determining averages in the preliminary results. 

Group II, was composed of thirty-eight persons, twenty-eight young 
men and ten young women, all students whose educational progress had 
been arrested, and who, at ages averaging about twenty-two, were en- 
deavoring to supplement their early schooling by two or three years 
of special study, part of it Biblical and looking toward some modest 
form of religious work. These students were in no sense below the 
normal in the development of general mental functions ; there were no 
cases of abnormal retardation ; only they had not had thorough earlv 
training. This group also was used only in results having to do with 
averages. 

Group III, was the largest and by far the most important group for 
our purposes. It was made up of fifty-eight boys and forty-eight girls, 
one hundred and six in all, being students in the seventh and eiehth 
grades Grammar and the following years of High School. Some of 
the members of this group did not take all the tests, although many of 
them did. In calculating results in terms of correlation coefficients 
members of this group were divided, selected and rearranged in smaller 
companies to meet the conditions involved. 

In stating the results the number of reagents involved is always given. 
It will be noticed that a number of the recorded results are based on 
smaller grouos taken out of this large company on a basis of uniformity 
in age or sex or both. 

29 



Group IV, is a little-used grouping of sixteen college students, eleven 
boys and five girls. This group appears only in the results in averages, 
which are only preliminary to the chief results of these experiments. 

Concerning all the subjects of these tests, it may be said that they 
were attending the same group of institutions, were all personally known 
to the writer and were all tested at practically the same time. 



3. APPARATUS. 

All the tests were made with extremely simple apparatus. This method 
represented a conclusion reached after a number of preliminary ex- 
periments. At first six or eight mechanical puzzles of varying degrees 
of difficulty were presented to about twenty high school students. But 
it required so much time to solve these, when they were solved at all, 
that it soon became evident that the result sought by this particular 
series of tests could not satisfactorily be reached in this way. For the 
same reason fairly complicated samples of geometrical puzzles were 
abandoned, and it was finally decided to use puzzles which practically 
every student could solve in a reasonable time (say fifteen minutes), 
but which none could solve without some degree of diligent mental 
application. 

The puzzles used were as follows : 

1. The Bird Puzzle. Cardboard pictures of two birds, a vulture, 
S l A x 6 inches, and a peacock, 5^4 x &/ 2 inches, were cut into five 
and seven cross-wise strips respectively, all the strips being of 
equal width. These twelve strips from the two pictures were 
then mixed, placed face downward, in a single pile and handed 
to the reagent to be matched. To insure the greatest uniformity 
of conditions the twelve strips were always piled in the same order — 
that indicated by the left hand figures on accompanying illustration (see 
Plate I, No. 1), number one was at the bottom of the pile and number 
twelve at the top, all face down. The reagents' task was to piece together 
in as short a time as possible the complete pictures of the two birds. 
The fact that there were two birds instead of one complicated the 
task somewhat. Nevertheless this was by far the simplest puzzle. 

2. The Match Puzzle. Seventeen matches were arranged in six con- 
tiguous squares (see Plate II, No. 1). The problem was to remove only 
five matches and leave intact three of the original squares. 

3. The Geometrical Puzzle. A piece of heavy plain cardboard 4^4 

30 



inches square was cut as indicated in Plate II so that the pieces 
could be readjusted in the form of a cross with arms 6^ inches across 
(see Plate II, No. 2). The parts were first placed in a cross form 
and the reagent was required to rearrange them into a square. One side 
of the cardboard was slightly tinted to keep the reagent from turning 
any piece wrong- side up. 

4. The Maze Puzzle. A maze was marked out in heavy black lines 
and placed under a ground glass cover in a wooden frame (see Plate I, 
No. 2). Starting from the arrow the reagent was to trace a continuous 
line through the open spaces to the dot in the center of the maze. It 
will be seen that very frequent choices have to be made, the number of 
choices depending upon the route taken. This particular maze was 
adopted after experiments with more complicated mazes as well as 
with simpler ones. 

Recent experimental psychology is demonstrating the fact that in most 
cases the most significant and trustworthy records of the deepest 
mental processes can be obtained by extremely simple apparatus 
just as well as by complicated apparatus. In fact the simple 
apparatus has an advantage over the more complex in that irrelevant but 
disturbing factors, some chiefly mechanical and some chieflv psychological 
are eliminated and the mental processes are thus allowed "to function all 
the more naturally. 



4. CONDUCT OF THE EXPERIMENTS. 

All the tests involving correlation were given in the same room and all 
within the limit of the same three or four days, with the exception of 
the repeated tests mentioned below. The room was of small size but 
fight, a pleasant corner room on an upper floor of the school building 
The room was unfurnished except for several tables and chairs All 
the tests were in private; the reagents were admitted to the room one 
at a time. No one was in the room with the reagent except the ex- 
perimenter. Silence was carefully observed as soon as each experiment 
was begun. While the reagent was at work the experimentor was 
generally busying himself figuring at a separate table or standing with 
his back to the reagent looking out of the window. 

The tests were taken voluntarily, and all the reagents were particularly 
requested to say nothing at all to anyone else about the experiments 

31 



until the sittings were all over. There is reason to helieve that this 
request was carefully honored. Reagents were frequently asked, for 
instance, before undertaking their work, whether any other student had 
said anything to them about the tests. Moreover it was observed that 
those coming later were not able to do the tests any more rapidly than 
those who first undertook them. 

When a reagent entered the room he was asked to seat himself at 
a table. He was told in a few words what was expected of him, em- 
phasis being placed upon the necessity of working the puzzle in as short 
a time as possible. The material was then put into his hand and his 
time was taken with a stop-watch. When he had worked the puzzle 
he said "Done" and his record was closed on the stop-watch. He was 
then, after a moment, moved to another table and started in the same 
general manner on the next puzzle. 

The puzzles were given in the following order: Bird Puzzle, Match 
Puzzle and Geometrical Puzzle. The Maze Puzzle was given on a later 
day. 

Instructions to reagents were practically as follows : 

Bird Puzzle. "I have here two pictures of animals cut up into strips. 
I wish you to take the strips and piece together both pictures as soon 
as possible. Just as soon as you have finished, say 'Done.' The point 
here is to have you do this just as quickly as possible." The reagent was 
then handed the twelve strips of the bird puzzle piled together face down- 
wards, and always arranged in the order indicated above. 

Match Puzzle. "Under this paper you will find seventeen matches 
arranged in six squares. I want you to remove five of these matches, 
without touching the other ones, so that you will have left three of the 
squares unbroken, but not more than three. When you finish, say 'Done.' 
You are to do this just as quickly as possible." A paper was then re- 
moved showing the seventeen matches arranged on the table. 

Geometrical Puzzle. "Under this paper you will find several pieces of 
cardboard arranged in the form of a cross. I want you to rearrange 
these pieces so as to form a perfect square, using every piece. Do it 
just as quickly as you can, and say 'Done' when you are through." The 
puzzle was then uncovered and the time taken. 

Maze Puzzle. "Here is a maze. You are to start your pencil here 
(showing him) and trace an unbroken line through the maze until you 
reach this center. As soon as you have found your way clear into the 

32 



center from the beginning, say 'Done.' Now do this just as rapidly as you 
can." The reagent's time was taken when the puzzle was handed him. 

In such ways as these an effort was made to standardize all condi- 
tions and to avoid the influence of irrelevant factors. Occasionally 
reagents would ask a question before proceeding with their work, but not 
often. ! ; ! 

Records were kept in a card-filing system, one card to each reagent. 
On each card was entered the name, sex, age, and general grouping 
of the reagent, and his time on every test he took. On the same card was 
also entered by number his rank or position in the General School, the 
Mathematical and the English rating. When anything went wrong in 
such way as to make questionable the value of the record, that particular 
record was cast out. On these record cards all lists and computations 
were based. 



5. METHOD OF OBTAINING SCHOOL RATING. 
" Since for the larger part of the tests the school rating of each reagent 
or group of reagents was one of the two terms between which correla- 
tion was sought, it was evident that care needed to be taken in procuring 
the figures representing this rating. The members of Groups I and II 
and IV were not given a school rating, but with the principle group 
(III) the rating was carefully worked out by combining several sets 
of data. 

First of all the monthly grades of all studies of every student for 
seven months of the same school year, the year during which these 
tests were made, were obtained from the regular school records, and these 
were averaged for each separate student. With this result was averaged, 
at a value of one-fourth, the average of all grades made by these students 
in the January term examinations. The studies thus counted in were, 
Foreign Languages, English Literature and Composition, Mathematics, 
Science and History. 

At the same time the teachers were asked to make lists of the students, 
graded as to general intellectual acuteness. The teachers were warned 
against basing their classification upon the students' general knowledge, 
which might have been accumulated in some cases only by very long 
and persistent study. The teachers particularly were asked to list the 
students as to their ability to see a point, to apprehend, their readiness 
to understand and to master new intellectual forms or content. The 

33 



teachers were asked to turn in their lists after working them over care- 
fully and regularly and in absolute independence. They were requested 
not to discuss this matter with one another in any form until the lists 
were all ready. These lists the Principal went over carefully, here and 
there, yet only in a very few instances, feeling obliged to alter the 
position of a student in any of the lists. After this a composite list was 
constructed which represented the average teacher-judgment as to the 
relative standing of each pupil in mental acuteness. 

There now were two general lists — one showing the grades of all 
the students as based on daily work, monthly tests, and one half-year 
examination; the other showing the consensus of judgment among the 
teachers as to the relative intelligence of the students. The remaining 
step was to combine these two listings of the same students. This 
resulted in one list, representing the average of these two, and in this 
list every factor used for determining the rating of a student played 
its part. This final list was designated School Rating, and is used as 
one term of the correlation in all comparisons making use of a student's 
intelligence as shown by his standing in his studies in general. 

It will be noticed that in a number of instances experiment results 
were correlated, not with the student's school rating in general, but with 
his school standing in a particular subject, mathematics or English. In 
such cases the school rating listing was of course not used, but a special 
listing which was made up of the student's record in that particular sub- 
ject, as indicated by an average of his daily work and monthly grades 
for seven months with one term examination. In these instances teach- 
ers' est : mates were not ascertained. 



6. METHOD OF CALCULATING RESULTS. 

Nearly all of the results in this paper are expressed in the form of the 
correlation between two sets of measurements, the measurement of school 
ability on one side and the measurement of speed in working out a par- 
ticular puzzle on the other. The resulting figure expresses the degree of 
correlation in a given group of students between these two measure- 
ments; jt shows to what extent the two abilities tend to agree. This 
figure is called the correlation coefficient. 

The particular formula used in obtaining this correlation is the one 

34 



first suggested by Spearman in 1904, 1 later simplified by him and sup- 
ported by abundant mathematical proof, 2 and a few years later carefully 
tested with satisfactory results by Burt. 3 

That some such precise method of ascertaining the exact relation be- 
tween two series of figures is a great improvement on the older ways 
is apparent almost without proof. Before a method of calculating cor- 
relation was worked out investigators in the field of psychological and 
related research could do little more than scan carefully the two series 
and endeavor to form some general impression of their relation to each 
other. Such lack of scientific method in securing results undoubtedly 
contributed much to the slow progress and frequent contradiction in the 
published results of research in psychology, not to speak of other de- 
partments of investigation. It has been demonstrated repeatedly that 
no amount of scrutiny of two series of figures can assuredly bring to 
light the presence or absence of definite correlation between them. 
Many times an array of statistics has been made the basis for a claim of 
overwhelming proof of correlation when a little actual figuring showed 
none to exist whatever. And on the other side correlation has frequently 
been altogether denied between two series which were found, upon 
calculation, to be very closely related. The crude method of dealing 
in general averages and the scarcely less crude method of arbitrarily 
dividing a series of results into such general groups as high, medium, 
low, or as good, fair, bad, and then comparing these artificial groups 
from one series with similarly determined groups from another series, 
have been able to give only approximate results in the most fortunate 
cases and misleading if not false results in the less fortunate cases. 

It was the realization of the utter unscientific character of such methods 
that led Bravais, Galton, and Pearson to devise what came to be general- 
ly called the "Standard Method" of obtaining a correlation result. This 
method, while it gave the desired preciseness, yet entailed such involved 
and laborious calculations, that it was highly desirable to work out 
some simpler though equally efficient formula. This was done by Spear- 
man. 

Spearman's method possesses the valuable features of being scientific, 
mathematical, simple of computation, of furnishing a formula applicable 
to many different kinds of results, of having a definite expression for 



(1) Amer. Jour. Psych. XV, pp. 72, 252. 

(2) British Jour. Psych. 1906, p. 89. 

(3) British Jour. Psych. 1909, p. 106 ff. 

35 



perfect correlation and a definite expression for the complete absence of 
correlation, of providing adequately for a valuation of probable error, 
and, finally, of being easily convertible into the coefficient of the "Stand- 
ard Method." 

A fundamental feature of Spearman's "foot-rule" for measuring cor- 
relation is the arranging of each series of values in a rank. One series 
may display results in special terms, another in time terms. Ordinarily 
these two would be incommensurable. By arranging each in a rank, 
however, it immediately becomes possible to compare one with the other. 
Absolute incommensurable quantities are converted into perfectly com- 
parable ranks. The highest result in the series is placed at one end of 
the list, the lowest at the other end, and each of the others in its proper 
rank between these two extremes. A given figure thereby loses, for 
purposes of correlation, its absolute quantitative value and takes on a 
relative value expressing its position in the rank. This procedure of 
course sacrifices for the time being a certain precision of quantitative 
information, but it makes possible the finding of an exact coefficient of 
correlation between two series otherwise mathematically unrelated. The 
possibility of exhibiting a precise relation between two such series is of 
immense value to experimental psychology. 

Since Spearman's method is the method by which the chief results 
in this investigation have been calculated, it will be well to explain the 
process, and in doing this, to make use of a simple example. Let us 
suppose that it is desired to measure the relation between keenness of 
hearing and tactual sensitiveness in a group of fifteen persons, A, B, C. 
. . .0. After experiment has determined the figures which represent 
each one's keenness in these two respects, a table is arranged as follows : 



36 



Example of Spearman's Foot-Rule 





1 


11 




REAGENTS 


RANK FOR 


RANK FOR 


GAIN OF 




HEARING 


TACTUAL 


II 






SENSITIVENESS 


OVER 
I 


A 


10 


II 




B 


II 


9 


2 


C 


3 


2 


I 


D 


12 


12 




E 


1 


I 




F 


4 


6 




G 


9 


10 




H 


2 


3 




I 


8 


8 




J 


14 


15 




K 


6 


7 




L 


15 


13 


2 


M 


7 


5 


2 


N 


13 


14 




O 


5 


4 


I 


15 






8 



Here A, B, C, etc., represent the different persons tested. In column 
I the figures represent the position of each person as arranged in a 
rank based on the results of the measurement of keenness in hearing; the 
best stands at 1, the poorest at 15. Column II represents by figures the 
position of these same reagents when arranged in a rank based on meas- 
urements of ability to distinguish two points placed near each other on 
the skin. Here the person showing the greatest discrimination (short- 
est distance between points) stands at 1, the reagent at the other extreme 
is listed as 15. In the last column the figures indicate how many points 
in rank any reagent gained in touch over hearing. 

Spearman's formula is R=i — — 2. . R=;correlation coefficient. 2p- 

M s ' 

the sum of the gains of one rank over the other — in our example, 8. 

M denotes the sum of the gains to be expected by mere chance. This 

?,7 



equals where n is the number of cases in the double series, 

in our example, 15. Applying this formula to the above example we 
find U=37-33 which gives us R = i— -— =—— = 0.71 +. Now 1.00 

would show perfect correlation, while 0.50 is considered a high correla- 
tion. Such a result as 0.71 therefore would be unusually high. 

But this result as it stands cannot be accepted as certain and final. 
The process must be tested for probable error. Spearman has demon- 

0.43, 
strated 1 that the probable error may be taken as being — = n again 

\ n 

being the number of cases. Working this out from our example we have 
0.43 0.43 n ,' . 

vl! = wr = - 114 

Now as to the value of the coefficient of correlation and probable error, 
as found by this method, Spearman declares that when a high correlation 
(R=o.5o or over) exists between two series, about a dozen cases are 
quite sufficient to prove this existence. The lower the correlation the 
greater the number of cases necessary ; as low a coefficient as R=o.20 
could not be proved with less than about one hundred cases. The 
value of even a few cases when the correlation is 0.5 or above to be 
borne in mind when the results of the present investigation are ex- 
amined below. 

As to the probable error, Spearman shows that it must be no larger 
than one-half as great as the correlation coefficient if the latter is to 
have any scientific value. Good evidence of the correlation calls for 
a probable error of only one-third or less. When it becomes one-fifth 
or less of R we reach a perfectly satisfactory demonstration. In view of 
these values our sample case is unusually strong, as it shows R=o.7i 
with a probable error of only 0.114. The coefficient results given for the 
investigations reported in this paper are all accompanied by an indica- 
tion of the probable error involved. 



7. DESCRIPTION OF RESULTS. 
Result 1. 
The reagents were divided into four groups representing different 



(1) British Jour. Psych. 1906, p. 106. 

38 



stages of mental development. Group III comprised 99 Grammar and 
High School students ; Group II, 38 older students whose earl} educa- 
tion had been cut short; Group IV included 16 college students; and 
Group I comprised 9 teachers, all below thirty-five years of age. All 
these persons were tested on the bird puzzle, the match puzzle and the 
geometrical puzzle, and the results for each of the four groups were 
calculated as to the average time, the median time and the mean variation 
from both the average and the median. This result was of course some- 
what preliminary, dealing in averages and not correlations. The intel- 
lectual homogeneity of each of the four groups was, however, to the 
personal knowledge of the writer, quite satisfactory, so that the results 
had some value after all. 









TABLE 1. 












Bird 


Puzzle. 






Group 


Reagents 


Av. 


Time 


M.V. 


Median Time 


M.V. 






Seconds 




Seconds 




III 


94 




95-58 


42.16 


75.00 


35-90 


II 


38 




95-42 


32.15 


86.00 


30.73 


IV 


16 




76.19 


22.68 


70.00 


21.56 


I 


9 




61.77 


1500 


60.00 


14.77 



These results are interesting in placing both in average and median 
time Groups III and II, both without advanced education, at the bottom 
of the list, while College students come next, with teachers safely in 
the lead. In both instances the academy students were most scattered, 
as shown by the mean variation, while the decidedly reduced mean varia- 
tion of the group of teachers increases the value of their record. 







TABLE 2. 
Match Puzzle 






Group 


Reagents 


Av. Time 


M.V. 


Median Time 


M.V. 


III 


44 


242.38 


165.43 


226 . 00 


165. 11 


II 


19 


214.00 


126.68 


201.00 


119-58 


IV 


16 


288.16 


206 . 00 


157-00 


189.81 


I 


9 


177.66 


196.00 


107.00 


123.77 



The general order of the bird puzzle is carried over into these results 
from the match puzzle. The lowest two are the untrained minds, while, 

39 



as before, the teachers are in the lead, in this instance even more so than 
before. 







TABLE 3. 










Geometrical 


Puzzle 






Group 


Reagents 


Av. Time 


M.V. 


Median Time 


M.V. 


III 


94 


120.49 


91-38 


68 


80.78 


II 


38 


55-8 


31-55 


48 


30.47 


IV 


16 


66.31 


5I.3I 


45 


39-56 


I 


9 


85.11 


H4-33 


222 


72.00 



In this experiment, the Academy students are again at the bottom and 
the college students next to the top. In the average time we find Group 
II in the first place and the teachers in the third, but the unusually large 
mean variation of the teachers' record tends to reduce the significance 
of this. In the median result, however, the teachers are far in advance 
of all, as before. 

So far as the general results of this experiment go, they tend to 
show that reagents with the least mental development are slowest at 
the tests, while those more advanced (college students) Come next, and 
those most highly developed (teachers) are in all but one instance most 
rapid at the puzzles. 

Result 2. 

Here the reagents were put into three groups on the basis of age, the 
youngest (Group 1) comprising the Grammar and High School students; 
the oldest (Group 3) the teachers, with the College and other young 
men and women in the intermediate class (Group 2). All three puzzles 
were worked with, and averages and medians calculated as in Result 1. 

TABLE 4. 

Bird Puzzle 

Group . Reagents Av. Time - M.V. Median Time M.V. 

I 94 96.58 42. 16 75 35.9 

H 54 90.64 29.79 80 29.16 

III 9 61.77 15. 60 14.77 

Here the average shows skill to increase with the age of the groups; 

40 



the median puts the youngest ahead of the middle class, but the oldest 



ahead 


of all. 














TABLE 5- 










Match Puzzle 






Group 


Reagents 


Av. Time 


M.V. 


Median Time 


M.V. 


I 


44 


242.38 


165-43 


236 


165. 11 


II 


3i 


I83-93 


121.00 


149 


in. 84 


III 


9 


177.66 


196.00 


107 


123.77 



These results worked out with complete regularity, in both median 
and average, to show an increase of skill with the increasing age of the 
group. 







TABLE 6. 










Geometrical Puzzle 






Group 


Reagents 


Av. Time M.V. 


Median Time 


M.V. 


I 


94 


120.49 9I-38 . 


68 


80.78 


II 


54 


59-i 35-34 


46 


33-13 


III 


9 


85.11 114.33 


22 


72.00 



Here, in the average the tables are turned upon the middle and oldest 
groups, but in the median the results indicate a substantial gain in skill 
with advance in the age of the group. 

All of Result 2, dealing only in averages and median and being based 
chiefly on differences in age, contributes but indirectly to our particular 
problem. This group of results goes to show, however, that age does 
not appear as a serious disturbing factor. It is worth noting as a partial 
explanation of the close identity between Results 1 and 2, that while 
in one the grouping is on the basis of intellectual development and in 
the other on the basis of age, yet for the most part these two features 
coincide in the subjects experimented upon, so that there was not much 
change of personnel in the different groupings for these two series of 
computations. 

Result 3. 

We now pass on to the more satisfactory mathematical methods in 

which the results are given as correlation coefficients. Result 3 expresses 

the correlation between the general school rating of 51 academy students 

and their rating on the bird puzzle. It gives us R=.62±.o6. This is 

41 



an unusually high correlation with an extremely low probable error, and 
thus it constitutes a significant result. 

Result 4. 

Thirty-three reagents, High School students. Correlation between time 
on match puzzle and school rating. R=.548±.075. A high corre- 
lation with a low probable error. 

Result 5. 

Correlation between geometrical puzzle and school rating of 51 High 
School students. R = .0262±.o6. High coefficient, low probable error. 

Result 6. 

A group of students were tested on their retention of the method 
of working these puzzles. When they first saw the match and the 
geometrical puzzles, nothing was said to them about any further test 
on these. But exactly one month afterwards they were called in and 
the same two puzzles were again placed before them without warning. 
They were then rated on the basis of their improvement over the first 
working of the puzzles as indicated by the reduction of their sitting 
time. This list of the time-gains was correlated with their school ra- 
tings. In connection with the match puzzle, we have 22 reagents ; R = 
.4i6±.o93. Not bad. 

Result 7. 
Time gained on geometrical puzzle correlated with school rating: 45 
reagents; R = .5i±.o64. Better still, with an insignificant probable 
error. 

Result 8. 
Here we have shown the correlation between the time listing of High 
School students on the maze puzzle and their school rating. Reagents 
55; R = .5411 ±.058. A safe result from all points of view. 

Result 9. 
These next five results substitute for the general school rating the 
students' rating in mathematics only, obtained in the same way as the 
general school rating except for the absence of the teachers' opinions. 
Result 9 shows the correlation between the match puzzle and this mathe- 
matical ability. Reagents 32; R = .5i9±.o76. 

Result 10. 
Geometrical Puzzle and mathematical ability; reagents 43; R = .52± 
.065. 

42 



Result ii. 
Correlation between mathematical rating and time gained on the sec- 
ond working of the match puzzle. Reagents 18; R = .38o9±.io. Not 
a valuable result due to the small number of reagents, rather low corre- 
lation and a high probable error. 

Result 12. 
Correlation between mathematical rating and time gained on second 
working of geometrical puzzle. Reagents 47; R =.5163:^.063. This 
is much better than the preceding result. 

Result 13. 
Correlation between mathematical ability and the record on the maze 
puzzle. Reagents 52; Rrrr .5394^.059. A strong result. 

Result 14. 
The next four results substitute a rating in English (Literature and 
Composition) for mathematics. Result 14 expresses the correlation be- 
tween English rating and the record on the Bird Puzzle. Reagents 53 ; 
R =. 5384^-059- 

Result 15. 
Correlation between English Rating and Match Puzzle. Reagents 25 ; 
R = . 5769+. 086. 

Result 16. 
Correlation between English Rating and Geometrical Puzzle. Re- 
agents 50; R = .575±.o6. 

Result 17. 
Correlation between English Rating and Maze Puzzle. Reagents 52 ; 
R = .55±.059. If all correlation of .50 or over is high, these mathe- 
matics and English results, taking into account also the low probable 
error, are safely above the line of uncertainty. 

Result 18. 
The remaining results (twelve in all) represent a still furth'er stand- 
ardization of conditions in that they are based on groups of students all 
within two years of age. This does away with the factor of age vari- 
ation and largely eliminates the element of age as a possible source of 
error. In no case did the ages of those in the group extend over two 
full years, although the exact limits of these two years vary slightly 
for the different groups. 
Result 18 shows the correlation between the school rating of a group 

43 



of boys and girls, all within two years of age, and their work on the 
bird puzzle. Reagents 24; Age 15-17; R = . 51 — -087. 

Result 19. 
Correlation between school rating of the same aged group and match 
puzzle. The reagents 13; Age 15-17; R = .5o±.i2. 

Result 20. 
Boys' and girls' school rating correlated with time of the group on 
geometrical puzzle. Reagents 27; Age 15-17; R = 497 2± -o83. 

Result 21. 
Same as above except with the maze puzzle. Reagents 26; Age 15-17; 
R=r.4844±.o84. 

Result 22. 

The following eight results retain the two year age restriction and 
include the additional feature of sex limitation. Each group consists 
hereafter of all boys or all girls, and all within two years of the same age. 
In this way the remaining factor of sex has been eliminated as a possible 
source of error. 

Result 22 represents the correlation between the school rating of a 
two year group of boys and their work on the bird puzzle. Reagents 
16; Age 15-17; R = . 36471b. 107. This is an unsatisfactory correlation 
coefficient with a dangerously large probable error. 

Result 23. 
Boys : Correlation between school rating and match puzzle. Reagents 
10; Age 15-17; R = 48±.i36. The small size of this group weakens 
the result. 

Result 24. 
The school rating of boys correlated with time of group on geometri- 
cal puzzle. Reagents 18; Age 15-17; R==.5747±.ioi. A strong result. 

Result 25. 
Group of two year boys : Correlation between school rating and maze 
puzzle. Reagents 16; Age 15-17; R=r.4ii7±.io7. 

Result 26. 
A group of girls all within two years of the same age. Correlation 
between school rating and bird puzzle. Reagents 16; Age 14^-16^; 
R = .3882±.io7. This coefficient is too low to be significant. 

44 



Result 27. 
Two year group of girls : School rating correlated with match puzzle. 
Reagents 16; Age 14^-16^; R = .3882±.i6. 

Result 28. 
Group of girls : Correlation between school rating and time on geo- 
metrical puzzle. Reagents 14; Age 14^-16^; R = .3538±.n. 

Result 29. 
Correlation between school rating and maze puzzle of two year group 
of girls. Reagents 11 ; Age 14^2-16^; R = .52:±.i3. 

Of these twenty-nine results here reviewed the first two, dealing with 
averages and medians, are quite satisfactory as far as they go, but 
their mathematical accuracy and consequent value does not by any means 
come up to the results of the twenty-seven following instances expressed 
in the form of correlation coefficients. 



45 









TABLE 


7- 










Exhibit o: 


All Correlation Results. 


- 










****** 


* 








Re- 




Correlation 






No. 


agents 


Sex Age 


Between 


AND 


R 


+ 


3 


5i 


Mixed 12-18 


School Rtg 


Bird Puz. 


62 


06 


4 


33 


Mixed 12-18 


School Rtg 


Match Puz. 


548 


075 


5 


51 


Mixed 12-18 


School Rtg 


Geom. Puz. 


6262 


06 


6 


22 


Mixed 12-18 


School Rtg 


Gain-Match P. 


416 


093 


7 


45 


Mixed 12-18 


School Rtg 


Gain-Geom. P. 


51064 


064 


8 


55 


Mixed 12-18 


School Rtg 


Maze Puz. 


54i 1 


058 


9 


32 


Mixed 12-18 


Math. Rtg 


Match Puz. 


5i7 


076 


10 


42 


Mixed 12-18 


Math. Rtg 


Geom. Puz. 


52 


065 


ii 


i8 


Mixed 12-18 


Math. Rtg 


Gain-Match P. 


3869 


10 


12 


47 


Mixed 12-18 


Math. Rtg 


Gain-Geom. P. 


5163 


063 


13 


52 


Mixed 12-18 


Math. Rtg 


Maze Puz. 


5394 


059 


14 


53 


Mixed 12-18 


Eng. Rtg 


Bird Puz. 


5384 


05 


15 


25 


Mixed 12-18 


Eng. Rtg 


Match Puz. 


5769 


086 


16 


50 


Mixed 12-18 


Eng. Rtg 


Geom. Puz. 


575 


06 


17 


52 


Mixed 12-18 


Eng. Rtg 


Maze Puz. 


55 


059 


18 


24 


Mixed 15-17 


School Rtg 


Bird Puz. 


5i 


087 


19 


13 


Mixed 15-17 


School Rtg 


Match Puz. 


50 


12 


20 


27 


Mixed 15-17 


School Rtg 


Geom. Puz. 


4972 


083 


21 


26 


Mixed 15-17 


School Rtg 


Maze Puz. 


4844 


084 


22 


16 


Boys 15-17 


School Rtg 


Bird Puz. 


3647 


107 


23 


10 


Boys 15-17 


School Rtg 


Match Puz. 


48 


136 


24 


18 


Boys 15-17 


School Rtg 


Geom. Puz. 


5747 


101 


25 


16 


Boys 15-17 


School Rtg 


Maze Puz. 


4117 


107 


26 


16 


Girls 14^-16^2 School Rtg 


Bird Puz. 


3882 


10 


27 


16 


Girls 14^-16^4 School Rtg 


Match Puz. 


388 


16 


28 


14 


Girls 14^2-16^ School Rtg 


Geom. Puz. 


3538 


11 


29 


ii 


Girls 14^-161/2 School Rtg 


Maze Puz. 


52 


13 



46 



8. SUMMARY OF RESULTS. 

When one glances down the "R" column of Table 7 (which exhibits 
all the correlation results) it is at once apparent that by far the larger 
part of the correlation coefficients are safely within what Spearman calls 
high correlation (.5 or above). The showing as a whole therefore is 
significant and worthy of attention. 

Spearman declares that a dozen cases are sufficient to establish a cor- 
relation of .50, due attention being given to the probable error. We 
have in this list of twenty-seven results, seventeen which show "R" = .5 
or above, and of these seventeen only one deals with less than twelve 
reagents — Result 29 being calculated on but eleven. Only two others 
have less than twenty-four cases (Result 19 with thirteen, and Result 
24 with eighteen). There are seven results with over fifty cases each, 
and we have an average number of 37.8 cases for the entire seventeen 
results. It would appear then that there is no question about the value 
of the results in sixteen of these seventeen cases (dropping No. 29), 
for they all meet the necessary conditions as to number of cases and 
most of them are far above what is required. 

Investigation of the probable error in these sixteen results shows that 
in each case it is safely below one-third of the correlation coefficient — ■ 
in fact in only one instance does it approach even one-fourth (Result 
19: R^.5±:.i2), while in the remaining fifteen cases it is less than 
one-fifth. From the point of view therefore of mathematical results we 
have at least sixteen cases of unquestionable significance, all based on a 
good number of reagents, all having a high correlation coefficient with 
a low probable error. 

Of those results which fall below R = .5 there are four which are too 
low to be considered, — viz.: No. 11, R = .3869; No. 22, R^.3647; No. 
26, R = .3882; and No. 28, R = .3538. Of the remaining we have No. 
20 (Reagents 27, R=:.4972±.o83), and No. 21 (Reagents 26, R = 4844 
± .084), which, on account of their close approach to .5, of the large 
number of cases in each and of the low probable error, may safely be in- 
cluded among the valuable results. It seems best, in order to be on the 
safe side, to throw out No. 6, No. 23, No. 25 and No. 27 because of the 
low coefficient (No. 6), the few reagents involved (No. 23), or for both 
these reasons (No. 25 and No. 27). 

What have we left then as a possible basis for declaring the existence 

47 



of a correlation between school intelligence and speed in working puz- 
zles? We have eighteen results, as shown in Table 8 which follows: 

TABLE 8. 
The Eighteen Accepted Correlation Results. 

Re- Correlation 

No. agents Sex Age Between and R ± 



3 


5i 


Mixed 


12-18 


School 


Rtg. 


Bird Puz. 


.62 


06 


4 


33 


Mixed 


12-18 


School 


Rtg. 


Match Puz. 


.548 


075 


5 


51 


Mixed 


12-18 


School 


Rtg. 


Geom. Puz. 


.6262 


06 


7 


45 


Mixed 


12-18 


School 


Rtg. 


Gain-Geom. P. 


•5i 


064 


8 


55 


Mixed 


12-18 


School 


Rtg. 


Maze Puz. 


■541 1 


058 


9 


32 


Mixed 


12-18 


Math. 


Rtg. 


Match Puz. 


•517 


076 


10 


42 


Mixed 


12-18 


Math. 


Rtg. 


Geom. Puz. 


•52 


065 


12 


47 


Mixed 


12-18 


Math. 


Rtg. 


Gain-Geom. P. 


•5163 


063 


13 


52 


Mixed 


12-18 


Math. 


Rtg. 


Maze Puz. 


•5394 


059 


14 


53 


Mixed 


12-18 


Eng. 


Rtg. 


Bird Puz. 


.5384 


059 


15 


25 


Mixed 


12-18 


Eng. 


Rtg. 


Match Puz. 


•5709 


086 


16 


50 


Mixed 


12-18 


Eng. 


Rtg. 


Geom. Puz. 


•575 


06 


17 


52 


Mixed 


12-18 


Eng. 


Rtg. 


Maze Puz. 


•55 


059 


i.8 


24 


Mixed 


15-17 


School 


Rtg. 


Bird Puz. 


•5i 


087 


19 


13 


Mixed 


15-17 


School Rtg. 


Match Puz. 


•5 


12 


20 


27 


Mixed 


15-17 


School 


Rtg. 


Geom. Puz. 


•4972 


083 


21 


26 


Mixed 


15-17 


School 


Rtg. 


Maze Puz. 


.4844 


084 


24 


18 


Boys 


15-17 


School 


Rtg. 


Geom. Puz. 


•5747 


101 



All of these eighteen results are significant since all have a safely 
secured high correlation coefficient. How are these results distributed? 
We find that ten of them deal with general school rating (Nos. 3, 4, 5, 
7, 8, 18, 19, 20, 21, 24), four each with mathematical rating (Nos. 9, 10, 
12 and 13) and English rating (Nos. 14, 15 , 16, 17). We find that two 
(Nos. 7 and 12) deal with the gain in time on the second working of a 
puzzle, in both instances the geometrical puzzle. We find that, all told, 
the Bird Puzzle figures in three of these results (Nos. 3, 14, and 18), 
the Match Puzzle in four (Nos. 4, 9, 15 and 19), the Geometrical Puzzle 
in seven (Nos. 5, 7, 10, 12, 16, 20 and 24) and the Maze Puzzle in four 
(Nos. 8, 13, 17 and 24). We find that of these eighteen positive results 



48 



only five have a strict age limit (Nos. 18, io, 20, 21 and 24), and of these 
five but one (No. 24) adds the further restriction of sex limitation. 
One result therefore out of the entire twenty-seven fully meets all con- 
ditions, i. e. reagents sufficient in number, restricted as to age and sex, 
coefficient above .5 with low probable error. This does not indicate by 
any means that all the other seventeen results of Table 8 are to be thrown 
out. Yet it does emphasize the fact that as the groups of reagents became 
more and more homogeneous, the evidences of high correlation become 
fewer. This may be due in part to the smaller size of the more restricted 
groups, or it may be due to the elimination by means of these restrictions 
of sources of error. We must not forget, moreover, that the positive 
evidence of this one result is sufficient to counter-balance a number of 
cases giving purely negative evidence. 

Turning now to a brief summary of the differences between general 
school rating, mathematical rating, and English rating it will be seen 
that on the whole general school rating comes out more often with a pos- 
itive result. Rut this may very likely be due to the fact that general 
school rating is used as a correlation member much oftener among the 
twenty-seven results than either of the restricted ratings. Wherever the 
English rating is used (Nos. 14, 15, 16, 17) it comes out with a coeffi- 
cient above .5. The same is true of four out of five occurrences of the 
mathematical rating, the failure (No. 11) being on the gain in the second 
working of the match puzzle. 

The average correlation coefficient for the different kinds of rating is 
found to be as follows : General school rating, R .4852 ; Mathematics 
rating, R .4959; English rating, R .5600. (See Table 9.) 

When we compare the entire result of the four different puzzles, we 
find that the Bird Puzzle gave a high coefficient in three cases out of a 
possible five ; the Match Puzzle in four out of a possible eight ; the 
Geometrical Puzzle in seven out of a possible eight, and the Maze Puzzle 
in four out of a possible six. 

In the same general order are the averages of all the results involving 
each separate puzzle. The average coefficient of all Bird Puzzles is R 
.4842; of all Match Puzzles, R .4766; of all Geometrical Puzzles, R .5216; 
and of all Maze Puzzles, R .5077. (For averages of correlations see 
Table 10). 

It is worth bearing in mind that the Geometrical Puzzle, and the some- 
what similar Match Puzzle (one of which deals with solid surfaces and 

49 



the other with boundaries), naturally call for more concentrated and 
comprehensive thinking than the simple Bird Puzzle, which is so largely 
a matter of visual perception, or than the Maze Puzzle, where one cannot 
well see the solution from the beginning, but must proceed for the most 
part from step to step. There is surely a larger element of chance in the 
Maze Puzzle than in any of the others, and a larger dependence upon 
the simplest forms of perception in the Bird Puzzle than in any of the 
others. While the Match and Geometrical Puzzles must of course use 
perception also, yet the imaginative, comparing, judging, and reasoning 
activities of the mind are in these two puzzles called into use much more 
than in either of the other two. 



50 



TABLE 9. 

Distribution of Results Among Ratings 

Rating Average Correlation. 



% ;j; ^ ^ s|s sjj % 



No 


Re- 


Sex 


Age Gen. School 


Mathematical 


English 




agents 






Rating 


Rating 


Rating 


3 


33 


Mixed 


12-18 


.62 






4 


33 


Mixed 


12-18 


.548 






5 


5i 


Mixed 


12-18 


.6262 






6 


22 


Mixed 


12-18 


.416 






7 


45 


Mixed 


12-18 


•5i 






8 


55 


Mixed 


12-18 


■54i 1 






9 


32 


Mixed 


12-18 




•517 




10 


42 


Mixed 


12-18 




•52 




11 


18 


Mixed 


12-18 




.3869 




12 


47 


Mixed 


12-18 




•5163 




13 


52 


Mixed 


12-18 




- -5394 




14 


53 


Mixed 


12-18 






.5384 


15 


25 


Mixed 


12-18 






•5769 


16 


50 


Mixed 


12-18 






•575 


17 


52 


Mixed 


12-18 






•55 


18 


24 


Mixed 


15-17 


•51 






19 


13 


Mixed 


15-17 


•5 






20 


27 


Mixed 


15-17 


•4972 






21 


26 


Mixed 


15-17 


.4844 






22 


16 


Boys 


15-17 


•3647 






23 


10 


Boys 


15-17 


.48 






24 


18 


Boys 


15-17 


•5747 






25 


16 


Boys 


15-17 


.4117 






26 


16 


Girls 


14^-16^ 


.3882 






27 


16 


Girls 


1454-16^ 


•338 






28 


14 


Girls 


i4^-i6 T /4 


•3538 






29 


11 


Girls 


14^-16^ 


•52 







Averages, 



4852 



•4958 



.5600 



5i 



TABLE 10. 

Distribution of Results among Puzzles 
Puzzle Average Correlation. 



No. 


Re- 


Sex 


Age 


Bird 


Match 


Geom. 


Maze 




agents 








Puz. 


Puz. 


Puz. 


Puz. 


3 


33 


Mixed 


12- 


-18 


.62 








4 


33 


Mixed 


12- 


-18 




.548 






5 


5i 


Mixed 


12- 


■18 






.6262 




6 


22 


Mixed 


12- 


■18 




.416 






7 


45 


Mixed 


12- 


18 






■51 




8 


55 


Mixed 


12- 


-18 








•54i 1 


9 


32 


Mixed 


12- 


■18 




•517 






10 


42 


Mixed 


12- 


-18 






•52 




ii 


18 


Mixed 


12- 


-18 




.3869 






12 


47 


Mixed 


12- 


■18 






•5163 




13 


52 


Mixed - 


12- 


-18 








•5394 


14 


53 


Mixed 


12- 


18 


•5384 








15 


25 


Mixed 


12- 


■18 




•5769 






16 


50 


Mixed 


12- 


■18 






•575 




17 


52 


Mixed 


12- 


■18 








•55 


18 


24 


Mixed 


15- 


17 


•5i 








19 


13 


Mixed 


15- 


■17 




•5 






20 


27 


Mixed 


15- 


17 






■4972 




21 


26 


Mixed 


15- 


•17 








.4844 


22 


16 


Boys 


15- 


■17 


•3647 








23 


10 


Boys 


15- 


17 




.48 






24 


18 


Boys 


15- 


17 






•5747 




25 


16 


Boys 


15- 


■17 








.4117 


26 


16 


Girls 


14/2- 


■i6/ 2 


.3882 








27 


16 


Girls 


14^- 


•i6/ 2 




.388 






28 


J 4 


Girls 


14^- 


■16^ 






.3538 




29 


ii 


Girls 


14/2- 


•i6/ 2 








•52 



Averages, .4842 .4766 .5216 .5077 

52 



9. CONCLUSIONS. 

When we endeavor to reduce the results of this series of experiments 
to definite conclusions we are soon ready to acknowledge that there 
are not a great many unqualified statements which can stand as being 
fully justified by the data gathered. The following, however, seem fairly 
to arise from the experiments reported herein : 

(i) The first results recorded, those dealing in averages and medians, 
point to the existence of a fairly close relation between school intelligence 
and the ability to work simple puzzles. The weakness here is not in the 
figures expressing these results but rather in the method pursued. 
Rough groupings and results in averages and medians, although widely 
used in this kind of investigation, "fall far short of reaching the exact- 
ness in results obtained by computing correlation coefficients. Taking 
these first two total results as they stand, however, there seems no good 
ground to question their testimony to the existence of such a close rela- 
tionship between school intelligence and the working of puzzles as we 
are investigating. 

(2) When we pass on to Results 3 to 29, which are calculated in terms 
of coefficient correlations we find only moderately satisfactory ground 
for supposing a substantial relationship to hold between school intelligence 
and the ability to work simple puzzles. When we take into account the 
fact that as the homogeneity of the groups increases the correlation co- 
efficient decreases, when we note that out of all these 27 sets of results 
there is only one where a high correlation is found in a group of the 
same sex and practically the same age, we are inclined to deny the exist- 
ence of any such correlation as we are seeking. This, however, would 
be going farther back than the data requires or warrants. There are 
at least 18 sets of results which must be reckoned with. We can only 
conclude that it is quite possible that school intelligence is represented 
on the average by rapidity in solving simple puzzles. We can not claim 
to have proved the presence of this relation in any constant high degree 
but we have established a probability in favor of its existence. 

(3) For the purpose of testing school intelligence the comparative 
value of the four different puzzles used seems to be established only to 
this extent : the geometrical and the quite similar match puzzles are the 
safest tests, the geometrical puzzle safest of all. Next comes the maze 
puzzle. Least valuable is the bird puzzle ; this is the easiest to work 
but has the least significance for our purpose. It seems, on the other 

53 



hand, that in the geometrical puzzle we are on the track of a test which, 
with more thorough and extensive investigation, may transpire to be of 
considerable value. This "lead" is worth following up. 

(4) As to the relative value of school rating, mathematical rating and 
English rating as one term of the correlation, representing school in- 
telligence, there do not appear to be sufficient grounds for any definite 
conclusion. Attention may be called to the higher average correlation 
of the English rating, but the significance of this for our purposes is 
largely offset by the fact that it can not represent school intelligence 
nearly as well as the school rating. This latter covers a good number 
of varied school subjects, instead of being confined to one, as is the Eng- 
lish rating, and it also finds approximately half its representative value 
in the estimate of students' mental acuteness by their teachers. 

(5) Another result worthy of mention is the obvious advantage of 
the correlation coefficient method over the cruder and more general meth- 
ods dealing in groups and averages. If we had only Results 1 and 2 
to deal with our conclusion would have been strongly in favor of a gen- 
eral and high relation between school intelligence and the working of 
puzzles, for certainly the average-results and median-results there record- 
ed go to establish this conclusion. But when we subjected the work 
of a large percentage of the same reagents to careful computation accord- 
ing to Spearman's "foot-rule" no results appeared which justified such 
a conclusion. Surely no one can question the far greater preciseness and 
certainty of results obtained in this latter manner. Consequently they 
have for us much higher value. When, for instance, we find that in a 
group of 18 students, of the same age and sex, there appears a correla- 
tion coefficient of .5774 with a probable error of only .101 (Result 24) we 
have the satisfaction of knowing that this figure stands for an incontest- 
ible fact, and a fact of great suggestiveness and representative value. 

(6) These conclusions seem to be more closely allied to the many 
researches in which no correlation has been found than to the one or two, 
notably Spearman's, in which an exceedingly high correlation has been 
claimed. As a matter of fact, however, the present investigation comes 
out midway between these two extremes. Its results are negative only 
in the sense of failing to approximate Spearman's almost perfect cor- 
relation. Instead of the great majority of the coefficient results running 
between .0 and .025 in this report it will be noticed that none go so low 
as this and that all are practically grouped around .5. Now .5 Spear- 

54 



man declares to signify "high correlation." As a matter of fact, of course, 
it indicates a position just half way between no correlation at all and 
perfect correlation. It is worthy of note, therefore that the present re- 
sults hold closely to Rrz^.5. This shows correlation, but not truly high 
correlation. 

(7) It would appear, then, that the relative position, of the members 
of a fair-sized and reasonably homogeneous group of young persons, 
as established by the time it takes them to work some simple sort of 
geometrical puzzle, will correspond fairly closely to the relative positions 
of these same persons in school intelligence. By "fairly closely" is 
meant that the correspondence will be materially more than half way 
between no correspondence at all and perfect correspondence. 



55 



CHAPTER IV. 

Second Experimental Series. 

AN INTENSIVE STUDY OF PUZZLE LEARNING 
WITH SPECIAL REFERENCE TO INDIVIDUAL DIFFERENCES 

and 
METHODS OF LEARNING. 

i. APPARATUS. 

The puzzles used in this series of experiments were greater in num- 
ber and variety than those used in the first series. They were all 
motor, however ; verbal and mathematical puzzles being excluded. 
These puzzles were in five groups, with two or three puzzles 
in each group. In all groups one puzzle was relatively easy and 
the other more difficult. In the last group the three puzzles were of three 
distinct grades of difficulty. 

GROUP I. 

Match Puzzles. 

i. Puzzle I. Matches were laid in 16 squares (see Plate II. No. i ). 

The problem was to remove only four matches and leave twelve of the 

original squares. There are several ways of doing this, the simplest of 

which is to remove the four matches in the center of the figure. 

2. Puzzle II. Matches were laid in six squares (see Plate II. No. 3). 
The problem was to remove five of the matches so as to leave three com- 
plete squares. The only way of doing this is indicated on the Plate. 

GROUP II. 
Geometrical Puzzles. 

3. Puzzle III. Five pieces of cardboard were laid in a strip. The 

56 



problem was to rearrange them all so as to form a perfect square (see 
Plate II. No. 4). 

4. Puzzle IV. Four pieces of cardboard were arranged in the form 
of a square (see Plate II. No. 2). The problem was to rearrange them in 
the form of a cross. 

In both these geometrical puzzles the cardboard was colored differently 
on the back side to prevent the reagent inadvertently turning a piece over, 
which would in most instances make it impossible to solve the puzzle. 

GROUP III. 
Tracing Puzzles. 

5. Puzzle V. A figure (see Plate I. No. 3) was placed under a 
ground glass cover in a wooden frame, and the reagent was asked to 
trace the entire figure in an unbroken line without going over any 
part more than once. 

6. Puzzle VI. The same problem as in Puzzle V, except with a 
different and considerably more difficult figure to trace (see Plate I. No. 
4). 

GROUP IV. 
Maze Puzzles. 

7. Puzzle VII. A rectangular maze was placed in the frame under 
the glass and the reagent was asked to trace an unbroken path through 
the open spaces from the outside of the maze to the center (see Plate 
I. No. 5). 

8. Puzzle VIII. The same problem as in Puzzle VII, except with a 
more difficult maze (see Plate I. No. 6). 

GROUP V. 
Metal Puzzles. 

9. Puzzle IX. Two heavy wire loops resembling horseshoes (see 
Plate I, No. 1) were placed in the hands of the reagent to be taken 
apart. 

10. Puzzle X. Two twisted nails (see Plate I, No 8) were given 
the reagent with instructions to take them apart. 

11. Puzzle XI. Two keys fastened together by their squares (see 
Plate I, No. 9) were laid before the reagent, who was asked to take 
them apart. 

57 



2. REAGENTS. 
There were in all eleven reagents. All of the puzzles in all their forms 
were given to each of these eleven reagents with one or two slight 
exceptions. One of the chief values in the results of this series of 
experiments lies in the unusually varied and representative features of 
this group of reagents. As to sex, six were male, five were female. 
As to age, the reagents ranged from the bottom to the top. One was 
6 years old, one 13, one 14, one 17, one 25, one 28, one 33, one 34, one 
35, one 45, and one was 70. Four were school children, seven were 
adults. A full appreciation of the results to be discussed later calls 
for a brief description of each one in this varied group of reagents. 

(1) Sb was a boy 6 years and 2 months old. Brighter than the 
average in school, as evidenced by the fact that at this age he was in 
the second grade in a small private but standardly graded school. Sb 
proved one of my most interesting cases, as will be shown below. 

(2) Bb, a boy of 13, a student in the first year high school, was ex- 
ceptionally good in his school gradings. 

(3) Bg was a girl of 14, selected because of her high standing in 
school. She also was in first year high school. 

(4) Db was another case of spec'al interest. A boy of 17 he had 
repeatedly proved himself a mischief maker in school, a leader of re- 
volt, and a general failure as a student. He had somehow managed 
to reach high school but had been dismissed from school on a number 
of occasions, sometimes for hopeless scholarship, sometimes for general 
incorrigibility. He had been reinstated on his earnest promise to do 
right, but had always soon brought suspension upon himself, and finally 
expulsion. These things need to be borne in mind when we come 
to examine his record. 

(5) Rd was another case of unusual value, being a marked ex- 
ample of retarded development. As a child he had endeavored to at- 
tend public school but was too slow and too much confused to fit into 
the machinery of the school room. He had, therefore, been kept at 
home and taught some things by his mother, whose intense sympathy 
tended to soften him rather than to spur him on to great endeavor. 
He had learned to read tolerably well and had read much in history, 
which interested him, and in the Bible- His reading ability at the age 
of 33 was equal to that of a fair 7th grade student. He could re- 
member but little of what he read. In figures he was unable to do 

58 



anything but the very simplest addition, no subtraction, etc., although 
several male relatives had labored long to teach him. Physically he was 
well and very strong, normal in all his functions, except with exagger- 
ated nocturnal emissions. Rd's general appearance was quite normal ; 
in the company of those not of his immediate family he was shy and 
awkward, with long stretches of inactivity and silence. Comparison of 
Rd's record with that of the others yields interesting results. 

(6) Mm, a young woman of 25 with a good business education and 
experience. 

(7) Mt, a young woman of 28 with general schooling. Mm and Mt 
are the only two reagents who are very much alike in general respects. 
Close comparison of their records on the tests thus approaches the 
"method of difference." 

(8) Ba, a man of 35, with a wide experience in life, recently earned 
the A.B. degree. 

(9) Mg, a married woman of 34, mother of several children, had had 
one or two years of schooling beyond high school. Mg was the mother 
of Sb, the 6 year old boy. 

(10) Pd, a man of 45, holder of four academic degrees including 
Ph. D. His case yielded some especially interesting results. He was the 
father of Bb, the bright boy of 13 years. 

(11) Gm, an elderly woman of 70; ordinary early education, was in 
full possession of all her powers, and was a great reader. Her record 
decidedly increases the range of the investigation. Gm was the mother 
of Mg, and thus the grandmother of Sb. We have then one instance of 
three generations in these records. 

These eleven reagents may be grouped for various purposes in differ- 
ent ways, viz. : 

1. Males: Sb, Bb, Db, Rd, Ba, Pd. 
Females: Bg, Mm, Mt, Mg, Gm. 

2. Retarded development Rd. 
Primary Sb. 

High school Bb, Db, Bg. 

Beyond high school, Mm, Mt, Mg. 

College degrees, Ba, Pd. 

3. Within the high school group,— bright Bb, Bg ; dull Db. 

4. Age, Sb 6 

Bb 13 

59 



Bg 14 
Db 17 
Mm 25 
Mt 28 
Rd 33 
Mg 34 
Ba 35 
Pd 4 5 
Gm 70 



3. PROCEDURE. 
A. In General. 
(1) Each reagent was tested privately. 

(r?) No sitting ran over 1^ hours. If more time was needed another 
sitting was arranged for. 

(3) Puzzles were presented in the order in which they are listed in 
the description of "apparatus" above. 

(4) Reagent was seated at a table. He received his instructions; 
the puzzle was laid on the table before him (or in the case of the 
matches, they were uncovered), and his time was opened on a stop-watch. 
When he finished his task he said "Done," according to instructions, 
and his record was closed on the stop-watch. 

(5) Each puzzle was presented in the same way to each reagent 
throughout its series, except that Puzzle II was always turned one-quarter 
way around after it was first successfully solved. 

(6) In addition to a time record, I listened for exclamations or re- 
marks from the reagent during the course of his work. 

(7) A record of false moves was also attempted. 

(8) Fatigue was watched for, and by occasional special inquiry was 
recognized about as soon as it appeared. It was thus possible to avoid 
irrelevancies due to this cause by discontinuing the immediate sitting 
as soon as fatigue appeared. 

(9) The reagent's instrospective report of how the puzzle was finally 
worked was also obtained. 

(10) Seven days after the reagents went through all the puzzles 
they were put through them once again, without in the meantime having 
been warned of this repeated test. 

Co 



B. In Particular. 

(i) The instructions were simple and brief. A few examples will 
suffice : 

(a) Puzzle I. "Here are matches arranged in 16 squares; remove 
any 4 matches so as to leave 12 complete squares. Do this as quickly 
as you can, and say 'Done' when you are through." 

(b) Puzzle III. "Here we have 5 pieces of cardboard forming a 
strip. Rearrange them so as to form a perfect square." 

(c) Puzzle VII. "Trace your way through the open spaces from 
the outside into the center of the figure." 

(d) Puzzle X. "Remove one nail from the other." 

(2) The reagent was first given the puzzle with such brief instruc- 
tions, but without any directions at all. 

(3) After he had either solved the puzzle or had failed and given 
up he was asked to listen to the reading of the directions, after which 
he was handed the puzzle to be worked again. The directions were 
about as plain as they could be without, being lengthy. It is important 
that these be known and they are therefore here given. 

(a) Puzzle I. "Remove the four matches in the center of the 
figure." There are several other ways to do this puzzle, and frequently 
a reagent had worked it without directions by one of these other methods. 

(b) Puzzle II. "Remove the middle match on one long side of 
the figure. Then remove the corner matches on both corners of the op- 
posite long side of the figure." 

(c) Puzzle III. "Place the small square piece somewhat diagonally 
for the center of the large square. Take one of the triangular pieces and 
place it up against one side of this small square so that its shortest side 
forms a direct continuation of a side of the "small square. Do like- 
wise with the remaining three triangular pieces." 

(d) Puzzle IV. "Notice that one of these pieces looks somewhat 
like an arrow-head. Take this and place it pointing upwards. Take the 
other large piece and fit it to the arrow-head by joining their longest 
edges one to the other. Take the next largest piece and put its longest 
edge to the remaining slanting surface of the arrow-head. Then add 
the small piece to the upper left-hand corner of the figure." 

(e) Puzzle V. "Begin at the top of the large triangle and run down 
the left side of the triangle, then across the bottom, then half way 
up the right side to where the inner triangle touches the outer triangle ; 

61 



at this point run on to the inner triangle and go completely around it, 
coming back to where it touches the right side of the larger triangle ; 
from here continue up this right side of the larger triangle to the top, 
then go around the circle." 

(f) Puzzle VI. ''Begin at the upper end oi the inside diagonal line, 
run down this diagonal, then run straight down to the circle, take the 
short diagonal line up to the right, cross to the left by the long straight 
line, take the short diagonal line down, run to the top by the long 
straight line, and keep this kind of route until you reach the upper end 
of the right-hand vertical line, then go around the circle, and come 
down this line to where the inner diagonal line runs into it." 

(g) Puzzle VII. "Throughout your course pass by the first open- 
ing from the outer into an inner square and always enter by the second 
opening you reach. As soon as an inner square is entered, always turn 
to the right of the direction you were going when you entered that 
square." 

(h) Puzzle VIII. "After entering the first square take the first 
opening into the next square ; to enter the next square take the second 
opening ; to enter the next square take the third opening ; to enter 
the next square take the third opening ; to enter the next square take 
the second opening ; to enter all the succeeding squares take the first 
opening. When you enter the outer square turn to the right; after that, 
upon entering a new square make every alternate turn to the right of the 
direction you enter, and the intervening turns make to the left." 

(i) Puzzle IX. "With the fingers of the left hand grasp one horse- 
shoe in the middle of the bend and hold in a horizontal plane with the 
opening toward the right. With the fingers of the right hand grasp the 
other horseshoe likewise and hold it in a vertical plane with the opening 
toward the left. Bring the longitudinal centers of the two horseshoes 
to the samejine and draw one from the other." 

(j) Puzzle X. "Hold a nail point in the fingers of each hand, and 
turn both heads straight up. Lift the right hand until the head of the 
right-hand nail passes over back of the other nail-head. Turn the right- 
hand nail so that its head will cut a semi-circle down toward the body, 
passing down to the left of the left-hand nail-head, and coming to a 
stop when pointing directly down. Throughout all this the position 
of the left-hand nail is not to be changed. Now push the two nails 
away from each other." 

62 



(k) Puzzle XI. "Notice that one key is larger than the other. Hold 
this large key in the left hand with its square on the side away from the 
body. With right hand hold shaft of other key straight up with its 
square towards the body. Now swing small key outwards and down until 
its shaft points straight down. Then twist it a half-circle to the left; 
which swings its square over the shaft of the larger key. Swing small 
key up towards the body until its shaft stands straight up. Then slide 
it to the left along shaft of large key. Swing head of small key in a 
semi-circle towards the body until it stands straight down. Twist it a 
quarter of a circle to the left and the points of its square pass out into 
the head of the large key. Work it around in the head until it escapes 
through the deepest of the four grooves." 

(4) After this the reagent was asked to read the directions once 
through to himself. Then he was given the puzzle to work the third 
time. 

(5) I then worked the puzzle before the eyes of the reagent, and im- 
mediately gave it to h'm to work again. 

(6) The last working of the puzzle was after I had helped the re- 
agent himself to do the puzzle with his own hands. We thus have the 
puzzle worked — 

(a) Without directions. 

(b) After hearing directions. 

(c) After reading directions. 

(d) After seeing the work done (demonstration). 

(e) After doing the puzzle himself and under guidance. 

(7) Between the different workings of the tracing and the maze 
puzzles all marks on the slate were washed off. 

(8) The three metal puzzles were always put back together out of 
the reagent's sight. 

(9) When the puzzles were again placed before the reagents after 
seven days the five different methods outlined above were once more 
used. 



TABLES 

Showing time records of each of the 11 reagents. Roman numerals 
on left margin designate the 11 puzzles as listed under "Apparatus" 
above. Numbers in parenthesis at head of the 5 double columns in- 
dicate the 5 methods of presentation as described under "Procedure 

63 



above. Column numbers in parenthesis are record of the control series. 
All time is, here given in seconds. "F" means failure. 









TABLE 


11. 










Rd. 








(I) 


(2) 


(3) 


(4) 


(5) 


I 


F(7) 


F(6) 


F(5) 


12(5) 


6(6) 


II 


F(F) 


F(F) 


F(F) 


F(n) 


16, F, 26, 9(F, 7) 


III 


F(6 3 ) 


FC113) 


F(i 7 ) 


F(i8) 


60, 32, 15 (14) 


IVa 


^3(90) 


24(16) 


20(11) 


18(12) 


19(10) 


IV 


F(95) 


F(95) 


F( 7 o) 


F(75) 


28, 12 (14) 


V 


F(6 7 ) 


F( 4 2) 


F(32) 


F( 3 6) 


35, 24 (30) 


VI 


F(F) 


F(F) 


F(F) 


F(F) 


75 (70) 


VII 


520(170) 


240(140) 


200(126) 


190(135) 


i75(i44) 


IX 


120(17) 


10(6) 


3(8) 


2(9) 


3(7) 


X 


F(43) 


F(i35) 


F(F) 


F(F) 


11, 16 (7, 24, 18, 8) 


XI 


F(i27) 


F(F) 


F(F) 


F( 5 2) 


195, 180 (42) 








TABLE 


12. 





(1) (2) (3) (4) (5) 

I 150 ( 3) 4(2) 3(2) 3(2) 3(2) 

II F ( F) F "( 4) F ( 3) 4 ( 3) 45 ( 2) 

III 107 ( 31) 35 ( 11) 130 ( 0) 285 (10) 45 ( 9) 

IV 53 ( 16) 185 ( 7) 15 ( 9) 14 (7) 13 ( 6) 
V 280 ( 92) 25 ( 18) 23 (15) 22 (14) 20 (14) 

VI 255 (165) 90 (170) 67 (27) 58 (25) 58 (22) 

VII 594 ( 57) 90 ( 46) 80 (44) 72 (41) 70 (43) 

VIII 230 ( 63) 180 (122) 140 (53) 133 (49) 130 (46) 

IX 87 ( 4) 4(3) 3(3) 3(2) 3(2) 

X F ( 37) 45 ( 6) 12 ( 3) 9(4) 6(3) 

XI 310 ( 54) 27 ( 16) 16 (14) 14 (11) 13 (12) 

64 



TABLE 13. 
Ba. 



(1) (2) (3) (4) (5^_ 

I 60 ( 3) 3(3) 3(2) 3(2) 3(2) 

II F ( 2) F ( 2) 6(2) 3(2) 3(2) 

III 134 (20) 35 ( 7) 12 ( 6) 7(5) 6(5) 

IV 11 (14)' 7(8) 7(7) 6(7) 7(6) 
V 36 (10) 15 (8) 12 ( 8) 12 ( 7) 11 ( 8) 

VI 342 (26) 92 (14) 20 (12) 18 (11) 17 (10) 

VII 58 (28) 30 (20) 25 (19) 23 (21) 20 (19) 

VIII 72 (37) 45 (36) 30 (30) 25 (24) 24 (21) 

IX 6(3) 4(2) 3(2) 4(3) 3(2) 

X 13 ( 6) 18 (38) 6(4) 5(3) 4(4) 

XI 337 (16) 18 (16) 16 (14) 18 (11) 15 (13) 



TABLE 14. 
Pd. 

(1) (2) (3) (4) (5) 

I F ( 6) 4(4) 3(3) 3(3) 3 ( 3) 

II F ( 48) 58 (5) 3(6) 3(4) 3 ( 3) 

III 405 ( 22) 45 ( 14) 3S ( 12) 37 ( 11) 30 ( 12) 

IV 48 ( 24) 14 ( 20) 10 ( 16) 9 ( 17) 10 ( 14) 
V 95 ( 70) 24 ( 61) 15 ( 4.9) 17 ( 42) 14 ( 37) 

VI F ( 85) 94 (60) 40 ( 54) 35 ( 50) 30 ( 53) 

VII 130 (130) 78 (125) 72 (104) 67 ( 92) 63 ( 88) 

VIII 120 (170) 98 (140) 84 (129) 81 (132) 80 (123) 

IX n ( 12) 6(9) 5(8) 4(7) 5 ( 5) 

X F (180) 62 ( 90) 13 (12) 5 ( 10) 5 ( 6) 

XI 92 ( 45) 70 ( 47) 44 ( 19) 24 ( 17) 18 ( 19) 

65 







TABLE 15. 












Bb. 








(I) 


(2) 


(3) 


(4) 
3 ( 3) 


(5) 


I 


600 ( 3) 


4 ( 3) 


3 ( 3) 


3 ( 3) 


II 


510 ( 15) 


22 ( 5) 


6 ( 4) 


3 ( 3) 


3 ( 3) 


III 


155 ( 19) 


18 ( 20) 


15 ( 18) 


14 (16) 


12 (15) 


IV 


21 ( 22) 


14 ( 7) 


13 ( 7) 


13 ( 6) 


12 ( 7) 


V 


155 ( 55) 


30 ( 28) 


22 ( 24) 


20 (27) 


20 (25) 


VI 


254 ( 45) 


400 ( 37) 


470 ( 33) 


49 (32) 


40 (30) 


VII 


165 ( 57) 


178 ( 42) 


80 ( 40) 


65 (38) 


54 (40) 


VIII 


300 (195) 


60 (163) 


58 (124) 


44 (60) 


40 (49) 


IX 


12 ( 4) 


2 ( 3) 


3 ( 2) 


2 ( 4) 


2 ( 3) 


X 


135 ( 85) 


54 ( 82) 


34 (212) 


11 (12) 


10 ( 1) 


XI 


F ( 30) 


40 ( 18) 


10 ( 20) 


8 (11) 


8 ( 9) 







TABLE 16. 












Db. 








(I) 


(2) 


(3) 


(4) 


(5) 


I 


75 ( 2) 


4 ( 2) 


4 ( 2) 


4 ( 2) 


3 ( 2) 


II 


4 ( 3) 


25 ( 2) 


2 ( 2) 


2 ( 2) 


2 ( 2) 


III 


246 (33) 


16 ( 7) 


16 ( 5) 


12 ( 4) 


10 ( 4) 


IV 


47 (10) 


8 ( 9) 


7 ( 8) 


6 ( 9) 


7 (88) 


V 


10 (15) 


8 (11) 


7 (12) 


7 ( 9) 


6 ( 9) 


VI 


67 (65) 


50 (30) 


3? (11) 


26 (12) 


22 (11) 


VII 


69 (19) 


37 (20) 


20 (18) 


18 (19) 


17 (17) 


VIII 


45 (40) 


34 (22) 


26 (18) 


24 (20) 


24 (19) 


IX 


6 ( 3) 


5 ( 3) 


5 ( 4) 


4 ( 2) 


3 ( 3) 


X 


65 (30) 


91 (45) 


50 (11) 


8 ( 6) 


4 ( 7) 


XI 


95 (12) 


38 (20) 


17 (13) 


11 ( 6) 


10 ( 9) 



66 









TABLE 17. 














Gm. 








(I) 




(2) 


(3) 


(4) 


(5) 


I 


56 (130) 


4 


( 3) 


5 ( 2) 


4 ( 2) 


3 ( 2) 


II 


F (360) 


F 


( 15) 


80 ( 6) 


F ( 5) 


F,i8 ( 4) 


III 


F ( 34) 


F 


( 15) 


44 ( 11) 


11 ( 8) 


10 ( 9) 


IV 


61 ( 56 


22 


( 35) 


18 ( 31) 


16 (23) 


17 (14) 


V 


128 (106) 


32 


(35) 


30 ( 30) 


22 (24) 


20 (28) 


VI 


210 (170) 


89 


(100) 


80 ( 90) 


72 (48) 


67 (35) 


VII 


140 (158) 


60 


(118) 


53 (101) 


50 (go) 


49 (84) 


VIII 


210 (116) 


90 


( 75) 


92 ( 60) 


84 (52) 


80 (59) 


IX 


5 ( 10) 


4 


( 5) 


4 ( 6) 


3 ( 3) 


4 ( 4) 


X 


F ( F) 


F 


( F) 


F ( 35) 


80 (18) 


72 ( 7) 


XI 


F ( F) 


F 


(280) 


F (210) 


F (40) 


90 (70) 







TABLE 18. 












Sb. 








(1) 


(2) 


(3) 


(4) 


(5; 


I 


- 25 ( 5) 


23 ( 4) 


6 ( 5) 


5 ( 3) 


4 ( 4) 


II 


F ( 3) 


70 ( 4) 


6 ( 4) 


6 ( 3) 


4 ( 3) 


III 


F (55) 


F (40) 


F (38) 


3i (26) 


26 (16) 


IV 


28 (18) 


24 (11) 


12 (12) 


8 (10) 


7 ( 9) 


V 


F (27) 


F (28) 


F (25) 


50 (36) 


41 (24) 


VI 


F (41) 


F (42) 


F (36) 


56,2 (40) 


4 (38) 


VII 


117 (44) 


75 (42) 


62 (40) 


60 (38) 


53 (33) 


VIII 


126 (78) 


100 (40) 


67 (30) 


47 (32) 


50 (28) 


IX 


4 (10) 


14 ( 2) 


7 ( 4) 


5 ( 3) 


3 ( 2) 


X 


7 (10) 


5 ( 5) 


5 ( 7) 


6 ( 4) 


4 ( 5) 


XI 


F (20) 


43 (14) 


28 (20) 


20 (15) 


19 (16) 



67 







TABLE 19. 












Mg. 








(I) 


(2) 


(3) 


(4) 


(5) 


I 


14 ( 2) 


2 ( 3) 


2 ( 2) 


2 ( 2) 


2 ( 2) 


II 


62 ( 5) 


8 ( 3) 


3 ( 2) 


4 ( 2) 


3 ( 2) 


III 


F ( 9) 


105 ( 7) 


11 ( 8) 


10 ( 7) 


9 ( 8) 


IV 


26 (27) 


12 ( 9) 


13 (10) 


10 ( 9) 


9 ( 8) 


V 


60 (22) 


11 (20) 


5 (18) 


5 (17) 


5 (15) 


VI 


75 (38) 


26 (26) 


19 (24) 


13 (20) 


10 (21) 


VII 


80 (51) 


45 (28) 


65 (26) 


50 (24) 


48 (21) 


VIII 


55 (35) 


90 (30) 


40 (30) 


to (25) 


42 (24) 


IX 


4 ( 2) 


3 ( 2) 


3 ( 3) 


2 ( 2) 


3 ( 2) 


X 


F ( 3) 


85 ( 4) 


7 ( 3) 


5 ( 2> 


6 ( 3) 


XI 


F (20) 


no (15) 


2-1 (II) 


13 (10) 


14 (i3) 







TABLE 20. 












Mi. 








(1) 


(2) 


(3) 


(4) 


(5) 


I 


54 ( 2) 


4 ( 2) 


2 ( 2) 


3 ( 2) 


2 ( 2) 


II 


120 ( 2) 


6 ( 30) 


3 (27) 


3 ( 3) 


3 ( 2) 


III 


152 ( 93) 


22 ( 24) 


18 (19) 


20 (11) 


17 (10) 


IV 


F ( 7) 


365 ( 3) 


3i ( 4) 


25 ( 3) 


18 ( 3) 


V 


70 ( 72) 


12 ( 7) 


10 ( 7) 


11 ( 6) 


9 ( 6) 


VI 


30 (172) 


10 ( 17) 


11 (11) 


10 (11) 


10 (12) 


VII 


89 ( 44) 


43 ( 36) 


30. (3^ 


28 (27) 


24 (25) 


VIII 


89 ( 50) 


74 ( 45) 


38 (42) 


39 (40) 


3i (36) 


IX 


23 ( 50) 


7 ( 6) 


4 ( 4) 


6 ( 3) 


4 ( 2) 


X 


F ( 12) 


90 (140) 


t6 (40) 


8 (15) 


6 (15) 


XI 


F (226) 


240 ( 30) 


210 (19) 


145 (15) 


90 (14) 



68 







TV 


^BLE 21. 












Mm. 








(I) 


(2) 


(3) 


(4) 


(5) 


I 


32 ( 6) 


8 ( 2) 


3 ( 2) 


3 ( 2) 


3 ( 2) 


II 


72 (25) 


3 ( 8) 


3 ( 3) 


3 ( 2) 


3 ( 2) 


III 


215 (24) 


100 (12) 


28 (11) 


20 ( 9) 


18 (10) 


IV 


F (13) 


45 ( 7) 


22 ( 6) 


9 ( 6) 


8 ( 6) 


V 


30 (14) 


10 (12) 


10 (10) 


9 (11) 


10 ( 9) 


VI 


375 (20) 


60 (18) 


12 (14) 


8 (16) 


8 (14) 


VII 


135 (34) 


80 (30) 


62 (28) 


30 (25) 


29 (24) 


VIII 


105 (40) 


100 (38) 


65 (29) 


35 (31) 


30 (28) 


IX 


35 ( 2) 


4 ( 3) 


4 ( 3) 


4 ( 2) 


3 ( 3) 


X 


F (60) . 


90 (11) 


16 (12) 


4 ( 9) 


5 ( 7) 


XI 


F (55) 


345 (30) 


290 (27) 


184 (28) 


60 (21) 



69 



4 . DISCUSSION OF RESULTS. 

I have given first of all the tables showing the time record of each 
reagent. The figures (i), (2), (3), (4), (5), across the top refer 
respectively to the five methods of working the puzzle, viz. : 

1. Without directions. 

2. After hearing directions. 

3. After reading directions. 

4. After visual demonstration. 

5. After solving it under guidance. 

Under these figures the first of each of the two columns shows the 
time in seconds on the first series of tests (the real experiments), the 
figures in parenthesis show the time on the control tests, 7 days later. 
"F" means failure. The roman numerals on the left margin indicate 
the eleven puzzles, as described above. 

A. PRELIMINARY. 

Before proceeding to discuss the results shown in these tables it is 
necessary to say a few words about the other attempted methods of 
recording results, dealing with false moves, exclamations, introspective 
reports, and fatigue. 

(1) First, as to the exclamations of the reagent during the course 
of a test (and under this word "exclamations" I include also all re- 
marks). Only in a very few instances did this record amount to any- 
thing. And this chiefly for two reasons. First of all, the exclamations 
were extremely few ; most of the reagents worked in perfect silence. 
To request exclamations now and then would have been to introduce 
an artificial and diverting element. The other reason why this method 
of seeking results amounted to so little was because when the exclamations 
were made they seldom were of such a nature as to throw any light 
on the mental processes functioning at that particular time. They were 
chiefly emotional, such as "Well!" "My!" "This is a tough one!" etc. 
Now and then a little information was revealed by such remarks as "Now 
I see it," "Here she comes," "At last !" etc., but in most instances 
such a course of events was indicated also by facial expression, or 
more generally by rapidity of movement to an immediate solving of the 
puzzle. What exclamations were of value will be noted in the discussion 
of the individual records below. 

70 



(2) The effort to keep an exact record of false moves was likewise 
exceedingly disappointing. And this for a number of reasons : for 
example, it was impossible to divide every series of movements into 
just so many moves; it was often difficult to tell whether a slight motion 
in the wrong direction, but immediately checked, was to be counted a 
move or not ; various moves would be right if they had been preceded 
by certain other moves, but not having been thus preceded, were they all 
to be counted false even though they were purposely aimed at the right re- 
sult? In short it was found quite impossible to reduce to any exact quan- 
titative expression the multitude of long, short, rapid, slow, accidental, 
purposeful, simple or complicated movements in the course of solving 
most of the puzzles. I had never before attempted any careful record 
of exclamations or false moves, but, encouraged by the report of Ruger, 
I had entered this undertaking with high hopes. My discovery of the 
seemingly insuperable difficulties involved was not, therefore, in ac- 
cordance with any mental prepossessions but rather contrary to such. 

(3) When the reagents were asked for a statement of their memory 
as to how they finally got through the puzzle, I occasionally got a gleam 
of real information, but seldom. In most instances they could not 
state any distinct memory. They had gone from step to step, often 
passing on by a mere chance move. In a few instances they had "seen 
through" the whole situation involved, but not often. Possibly the 
greatest regularity was in the case of the maze puzzles where a number 
of the reagents soon discovered that some of the openings from an outer 
to an inner square led to "blind alleys," and they therefore learned 
to run their eye on in advance to reconnoitre before tracing a line through 
an opening. None of them discovered for themselves the underlying prin- 
ciple of even the simpler maze ; the nearest to it was Db's observation 
that he went as far as he could before turning from one square into 
the next one. Of course the reagents had not been requested at the 
beginning to make special note of the way they solved their puzzles 
so as to report. Such would have proven a diverting element. As to the 
introspective reports then we may say : they seldom were definite, and 
wherever at all definite the reports of the different reagents were in 
quite general disagreement. This method contributed nothing positive, 
unless it be that feature on which there was the least disagreement, 
namely, that most of the puzzles had finally been solved by the "I don't- 
know-how-I-did-it" method. This does not mean, however, that chance 

71 



was the only factor in the solving, individual time records were too 
much in agreement to admit this. 

(4) As to fatigue, its influence was avoided as much as possible, as 
indicated above. The one exception to this rule was in the case of 
Mg, who became weary and nervous when about two-thirds through the 
sitting. She was continued, however, to the end of all the puzzles, and 
it is difficult to see any noticeable effect of this upon the time record of 
her last 3 or 4 puzzles. Her failure to get puzzles X and XI without 
directions is not far different from the experience of other reagents. 
See, for instance, Sb, Bb, Bg, Mm, Mt, Rd, Pd, and Gm. 

B. INDIVIDUAL RECORDS. 

Based on the Real Experiments. 

There remains only one basis of study which is exact, definite and 
continuous throughout, namely, the time record. On this as a basis let 
use note first of all some comparisons of the work of different reagents, 
making use of what exclamations or introspections we can as we pro- 
ceed. 

(1) Taking the high school group we have two boys and a girl. 
Of these one boy and the girl, Bb and Bg, were especially bright in 
school work, while the other boy, Db, was dull and disobedient, as de- 
scribed above. As to the two bright students, there is not a great deal 
of difference between them. The girl was somewhat the better student 
but the boy did better on the puzzles without direction. The girl failed 
in two puzzles, the boy in only one ; but that one the girl had done. 
Of those puzzles in which both succeeded the girl's total time was 1756 
seconds, the boy's 1662. The surprise comes when we compare the work 
of these two bright students with that of the incorrigible and slow- 
minded (school mind) Db. He is in every respect ahead of both the 
others. He did not fail in the working without directions of a single 
puzzle, and, furthermore, in only one puzzle is he slower than both the 
others (III) and in only one other puzzle is he slower than either one 
of the others (IV). A glance at these three tables will show how 
very much quicker than the other two Db was in nearly all the puzzles. 
For instance, Puzzle V, Bb 155, Bg 280, Db 10. Again Puzzle VIII, Bb 300, 
Bg 230, Db 45. Db's total time in the 8 puzzles done by all these three 
reagents was only 565, approximately 3 times as fast as the others. 
Nor do we find Db's lead confined to any special class of puzzles. He 

72 



excells in them all, with the exception of the simpler tracing puzzle. In 
.one other respect Db excells his two bright fellow students. It will 
be noticed that it took Bb the second solving to give him a real grip of 
Puzzle II, the third solving for Puzzle VI, the third for Puzzle X, and 
the second for Puzzle XI. Likewise Bg failed absolutely on Puzzle II 
until the fourth attempt, and then at her next try she ran up from 4 
seconds on the fourth to 45 on the fifth. Moreover she did not really 
grasp Puzzle III until the fifth solving, Puzzle IV until the third, Puzzle 
X until the third, and her fifth result on Puzzle VIII was still away up 
at 130. Now with all this slow and uncertain learning compare Db's 
record and we find only three such instances, and none of them ex- 
treme: Puzzle II needed a second try to fix its method (due undoubtedly 
to turning it quarter-way around), Puzzle X needed three solvings 
and Puzzle XI two, before Db was master of them. All this constitutes 
a remarkable record for such a scholastic and disciplinary outcast. In 
fact we may anticipate coming discussion and say that without any 
question the figures of Db make decidedly the best record of the entire 
group of eleven reagents, young and old. Here is ground for some 
valuable pedagogical research. 

(2) Let us next look at the record of the two college graduates, Ba and 
Pd, the latter a man in his prime, holder of four degrees. On the whole 
Ba's record is above the average. Most of his initial times are brief. 
He failed in only one puzzle. This becomes interesting when we note 
that it was the second match puzzle and was worked successfully by 
both the high school boys and by all three of the middle-aged 
women. All the weaker reagents, however, failed in this puzzle, that is, 
the 6 year old boy, the retarded development reagent and the aged woman. 
Why is this college graduate's generally excellent record weakened by 
such an inconsistent thing as agreement with the worst records in this 
comparatively simple puzzle? That his failure is not some sort of 
mistake is shown by the fact that even after hearing the directions read 
he failed again. 

(3) When we pass on to our university man, Pd, we are surprised to 
find his record the weakest of all outside our three abnormal cases (the 
small boy, the old lady and retarded development reagent). Pd has 
four initial failures — Puzzles I, II, VI and X. Puzzle X is admittedly 
difficult ; and yet it was done by Ba, Bb and Db, the latter two high 
school students, and, what is still more interesting, by the small boy 

73 



Sb in 7 seconds. Pd's failure in Puzzle VI, the second tracing puzzle, 
puts him in this item below Ba, below all three high school students, 
below all three of the middle-aged women, and even below the 70 year 
old woman, who solved this puzzle in 210 seconds. As to Pd's failure in 
both the match puzzles, it only goes to weaken his record the more. 
The retarded development reagent was the only other person failing in 
both these match puzzles. No one else at all failed in the first, and only 
Ba, Sb, Bg, in addition to Rd, agreed with Pd in failing in the second. 
Judged objectively Pd had by far the best mind of all the reagents, 
and yet in four out of the eleven puzzles he is completely outstripped by 
most of the others. Here we have another problem. 

(4) It will be interesting to examine the record of Gm, the 70 
year old woman. Her initial failures are four, Puzzles II, III, X and 
XI. In the first two instances she failed also after hearing the direc- 
tions read ; in Puzzle X she failed the third time, after reading over 
the directions herself ; and in Puzzle XI she continued to fail until she 
herself had worked the puzzle under guidance. The significance of 
such, figures will be discussed below when we come to study the results 
of these five different methods of learning puzzles. It will be not'ced 
that, with one exception, as soon as Gm got the idea of a puzzle she 
worked it thereafter with no hesitation above that due to lack of practice. 
She approximated her physiological limit as soon as she had once 
solved the puzzle. The exception is in Puzzle II. There she worked it 
in the slow time of 80 seconds after hearing the directions read, and 
her fourth and fifth attempts were failures, she requiring to solve it 
under direction the second time before mastering it, as shown by her 
next record of 18 seconds. Taking Gm's record as a whole it is un- 
expectedly good in view of her advanced age. 

(5) We now swing to the other extreme and consider the work of Sb, 
the 6 year old boy. Here there are surprises. For instance there are only 
five initial failures. Rd has eight, Gm four, each of the middle-aged 
women three, and even the scholarly Pd has four. Moreover this lad 
solved several puzzles where others failed, even not counting Rd. He 
solved Puzzle I where Pd failed. He solved Puzzle IV, the second 
geometrical puzzle, where Mm and Mt failed. In Sb's case, however, 
this puzzle was reversed, he being shown the cross and asked to form 
the square. Moreover Sb solved Puzzle X, the twisted nails, when Mt, 
Mm, Mg, Gm, Bg and Pd failed. That Sb's working of this puzzle was 

74 



not by chance seems indicated by his low initial time, 7 seconds, 
which was more than maintained by his subsequent trials of 5, 5, 6 and 
5 seconds respectively. There are only three puzzles in which Sb re- 
quired more help than the hearing or reading of the directions in order 
to be able to do the puzzle. In all these three (Puzzles III, V and VI) 
the technical nature of the directions was too much for him to grasp. 
Again, Sb's initial time in those puzzles which he did work without 
any directions is unusually low, for instance, 25, 28, 117, 126, 4 and 
7 seconds. Of this list the first item only is longer than the general 
average of the other reagents, the other times are as good as the average 
or, in some instances, better. Bg for instance took 594 seconds on 
Puzzle VII, Bb 167, Gm 140, and even Pd 130, while Sb got through 
in 117 seconds. On the whole the record of this small boy is quite sur- 
prising. He was taken up at first with only a faint hope of any results 
beyond continuous failure, but he has proved to be one of the most il- 
luminating and valuable cases. 

(6) We now pass to the record of Rd, the 34 year old case of re- 
tarded development. Here we find almost unbroken failure until the 
fifth trial, and in one instance (Puzzle II) until the seventh trial. The 
additional figures under the fifth column of Rd's record represent his 
work on trials beyond the fifth. Before each of these additional trials 
the reagent was once more put through the working of the puzzle with 
his own fingers, under guidance. In Puzzle IVa, the figure was reversed 
for Rd as for the 6 year old boy — he was shown a cross and asked to 
rearrange in a square. Rd was however also tried on Puzzle IV in its 
regular form. Puzzle VIII, the second maze puzzle, was omitted with 
Rd. It will be noticed that this reagent worked by himself only Puzzles 
IVa, VII (first maze) and IX (horseshoe) ; on all the others he failed 
repeatedly.' This is in striking contrast with the records of the 70 year 
old woman, of the 6 year old boy, and most of all with the record of 
the dull and incorrigible high school student, whose work in the puz- 
zles leads the entire group. It is perfectly evident from these results 
that there is an intellectual gulf between the young man of retarded 
development and even the little boy. In fact Rd's mental isolation could 
hardly be more graphically or conclusively set forth than by these com- 
parative records of definite quantitative results. Outwardly his actions 
are reasonably normal for a quiet, reticent person, but the puzzles re- 
veal a totally unsuspected degree of psychical abnormality. The other 

75 



chief contribution of Rd's case is in connection with the method of 
learning puzzles, which will be discussed in its proper connection. 

(7) Before closing this review of personal differences, as revealed 
by the puzzles, it will be interesting to glance at some comparisons 
within families. I purposely secured as reagents two generations in one 
family and three in another. Bb was the 13 year old son of Pd. A 
comparison of the record of these two reagents shows the son to be 
more successful at puzzles than his father. Both as to the number of 
failures, as to the length of the initial time when the puzzle was worked 
without direction and as to the time required for the fifth or last 
working of the puzzle, the son shows up better than the father. The 
father leads, however, in the readiness with which a puzzle is grasped 
after directions are given. In five instances (Puzzles II, VI, VII, X 
and XI) the son required more than one giving of directions to bring 
him to a mastery of the puzzle. There are but four of such instances 
in the record of the father, and of these only two (Puzzles II and X) 
are serious. The other family group was comprised of Gm, the mother of 
Mg, who in turn was the mother of the 6 year old Sb. Here it is 
sufficient to note two things. First, the middle-aged woman surpasses 
her 70 year old mother, as might be expected. Second, the record of 
the young boy comes close to that of his grandmother in many respects, 
and in a few points surpasses it. For instance his initial time on Puzzle 
I is less than half his grandmother's time. The same is true of Puzzle 
IV. And in Puzzles VII, VIII and IX his time is also less, although 
not by so great a margin. A comparison of final times shows him to 
be decidedly below his grandmother in six instances, viz. : Puzzles II, IV, 
VI, VIII, X and XI. 

The foregoing discussion should be sufficient to outline the leading 
results having to do with individual differences. Let us now consider the 
records from another point of view. 

C. METHODS OF LEARNING. 
Based on the Real Experiments. 

This section of the discussion deals with the relative value and signifi- 
cance of the five different methods of learning to solve puzzles. These 
five, it will be remembered, are (1) without any directions, (2) after 
hearing directions, (3) after reading directions, (4) after seeing the 

76 



demonstration, and (5) after solving the puzzle oneself under guid- 
ance. 

(1) A statistical exhibit may serve as the first grouping of results 
under this head. The number of times each of these five methods was 
followed by the first actual solving of the puzzle, taking into count all 
reagents and all puzzles, is as follows : 

(1) Without direction, 87 times. 

(2) After hearing, 19. 

(3) After reading, 2. 

(4) After demonstration, 4. 

(5) After doing, 10. 

(2) These figures, however, are somewhat misleading in this form. 
The test of a really successful method of learning is, it would seem, 
not so much the ability to work the puzzle after a good length of time 
but rather the ability to work it intelligently, which must mean promptly. 
We must pass on then to ask, how often did each of these five methods 
prove to be the immediate antecedent of a prompt and ready working of 
the puzzle, with a time reasonably near the reagent's physiological limit? 
Only such a test can reveal the fact that the reagent has actually grasped 
the idea or principle of the puzzle as a whole. To illustrate — we find that 
on Puzzle III Mg failed at first, succeeded in 105 seconds on the second 
trial and then made the remaining three trials successfully in 11, 10 and 
9 seconds respectively. Now it is obvious that the real mastery of the 
puzzle came at the third trial, when the time dropped suddenly from 
105 seconds to 11 and stayed there. In this particular stage of our 
inquiry we can disregard method (1) (without direction), and compare 
the value of the four methods which were based on directions in some 
form. Of course it stands without discussion that most of the puzzles 
were grasped without directions; but we now raise the question. If 
one cannot learn how to master a puzzle for himself what is the best 
method of being taught how to master it? Here our results are differ- 
ent from those of the preceding table. Real puzzle mastery was at- 
tained by the different methods with direction as follows : 

(2) After hearing, 41 times. 

(3) After reading, 19 times. 

(4) After demonstration, 8 times. 

(5) After doing, 11 times. 

77 



(3) But even this exhibit does not finally represent the underlying 
facts. Many of the 41 instances of success under method (2) followed, 
not a complete failure, but a self-working of the puzzle, without di- 
rections, one, however, that took so long as to reveal a total absence 
of real mastery. So method (2) in these cases comprised in truth 
much more than the mere hearing of the directions read : it was the 
hearing of the directions plus the visual and motor memories of hav- 
ing actually solved the puzzle with one's own hands just previously. 
To be sure the time on these particular initial solvings was always 
very great. But this does not mean that all this time was occupied 
in actually solving the puzzle. Most of the t ; me was taken up in ex- 
perimenting with false moves, but when the correct way was struck 
the puzzle was then solved very promptly. Method (2), then, is far 
from being a pure method of auditory directions. No one can doubt 
that the experience of having just worked the puzzle added far more 
to the mastery of the process as shown under method (2) than did the 
hearing of the directions. This point is easily proved by a further 
comparison of figures. Mastery of a puzzle first appeared under method 
(2) in 41 instances. But in 40 of these instances the puzzle had been 
previously worked out by method (1), although with a long time record. 
There remains, then, only a single instance (Pd Puzzle I) where method 
(2) gave a mastery of the puzzle when only failure had resulted under 
the first method. There are 8 cases which some might wish to add to this 
solitary instance, viz. : Sb XI, Mm IV and XI, Mt XI, Bg X, Bb XI 
and Pd VI and X ; but the time record in all of these under method (2) is 
so high compared with the minimum reached under later methods that 
it seems impossible to claim that in any of these cases real mastery 
was obtained under method (2). Let us, then, make one more exhibit, 
and let us show in this how many times each method resulted in im- 
mediate mastery of a puzzle, when all preceding methods had resulted in 
failure. This ought to give us the unmixed value of each separate 
method. The result is as follows : 

(2) After hearing, 1 time (Pd I). 

(3) After reading, 1 time (Ba II). 

(4) After demonstration, 3 times, (Sb V, Rd II, Gm X). 

(5) After doing, 11 times (Sb III and VI; Rd II, III, IV, V, 

VI, X and XI; Gm II and XI). 
It might appear at first sight that Bg on Puzzle II should be in this list 

78 



under method (4) (time, 4 seconds) ; but the time of 45 seconds in the 
next trial shows that the puzzle had not yet been truly mastered by 
method (4). This last exhibit is exceedingly instructive. It demon- 
strates the unquestionable superiority of method (5) in leading to a 
prompt mastery of a puzzle when previous methods have proved un- 
availing. Nor does the fact that with Gm Puzzle II had to be repeated 
once by method (5) and with Rd the same Puzzle had to be repeated 
twice by the same method before success came, in any wise reduce the 
great lead of this particular method. The solitary instances under method 
(2) and (3) respectively are practically negligible. The three cases 
under method (4) reveal some real value in that method, but they are 
not to be compared with the value of method (5). 

(4) It should be noticed that the eleven cases just discussed under 
method (5) are all taken from the records of Sb, Gm and Rd — the 6 
year old boy, the 70 year old woman, and the retarded development re- 
agent. The three cases under method (4) are also from these same 
persons. Inasmuch as these were the three reagents who might be 
called abnormal, these facts are worthy of note. How then, we may 
ask, did the normal reagents learn? This question is partly answered 
by the exhibits in paragraphs 1 and 2 above. And yet we must remem- 
ber that the exhibit in paragraph 3 shows all the instances where a 
prompt mastery of the puzzle followed previous failure to learn Out- 
side of these 16 cases the learning was gradual. This means that while 
two or more methods contribute toward the mastery, no single one led 
directly to it. Every repetition of the directions or of the labored 
working out of the puzzle helped bring the reagent to a mastery. To 
credit the mastery to the last one of several cumulative methods in 
cases like these would be an ungrounded conclusion. It is interesting 
to note that of the 121 instances of learning a puzzle (that is 11 puzzles, 
times 11 reagents) 11 times the mastery was gained in the initial 
working of a puzzle, JJ times the mastery came suddenly later in the 
series, while 2>2> instances do not show any sudden grasping of the situa- 
tion at all, but indicate a quite gradual learning. 

(5) These tabulated results reveal a peculiar feature of the learn- 
ing process. More than once a low time record seemed to indicate that 
the puzzle had been mastered. But we are immediately surprised to 
find the following time record jump to a high mark. This phenomenon 
appears, for instance, in the records of Bg, Puzzles II, III and IV; 

79 



Gm, Puzzle II; Db, Puzzle II; Sb, Puzzle IX; Bb, Puzzle VI, and in 
a number of other places. Bg explained this lapse, introspectively, by 
saying that she had learned the puzzle in question under one method 
but the presentation of a new method confused her. This cannot be 
accepted, however, without much question, since the procedure of solv- 
ing each puzzle was the same throughout, and the methods were not 
different ways of solving the puzzle but different ways of presenting to 
the reagent exactly the same form of procedure. It seems quite evident 
that the solution had not been truly mastered until all great rises in 
the time record ceased to appear. 

D. SUPPLEMENTARY TESTS. 
On Methods of Learning. 

This seems to be the best point at which to introduce the results of a 
brief series of supplementary experiments, arranged with the particular 
purpose of separating entirely the motor and the visual methods of 
learning. It will be noticed of course that in all the results discussed 
above every instance of the actual working of a puzzle (motor experi- 
ence) was done with eyes open and thus involved an additional element, 
i. e., visual experience. An effort was made to separate these two forms 
from all other kinds of learning. This necessitated arranging a new set of 
tests. 

(i) The puzzles used here were the three metal puzzles numbered 
IX, X and XI in our list above — the horseshoe puzzle, the twisted nail 
puzzle and the key puzzle. 

(2) The reagents consisted of 20 persons all near 25 years of age, 
10 of these were men and 10 were women. 

(3) The procedure was two-fold. One part consisted in taking one of 
these reagents and working before him one of the puzzles, he watching 
the process, but not being permitted to handle the puzzle, and then 
he asked to work it himself as quickly as possible, his time being taken 
on the stop-watch. The other part of the procedure consisted in blind- 
folding the reagent and guiding his fingers through an actual working of 
one of the puzzles. After this learning experience the blind-fold was 
removed and the reagent was asked to work the puzzle as rapidly as 
possible, an exact record being made of his time. In every instance the 
learning process covered two workings of each puzzle, either by the 
visual or the motor process, as the case might be. 

80 



(4) Puzzles and procedure were alternated so that the following 
conditions were obtained: (a) each of the 20 reagents worked all three 
puzzles; (b) no reagent worked any puzzle both ways; (c) each re- 
agent worked some of the puzzles after visual learning and the rest 
after motor learning; (d) total records were obtained for an equal num- 
ber of visual and motor cases; (e) and also an equal division of the 
tests between the men and the women. Thus for each of the 3 puzzles 
we have 10 visual records and 10 motor records, 5 of each being men, 
5 women. For all the puzzles we have 30 visual records and 30 
motor records, equally divided among men and women. The record 
tables follow : 

TABLE 22. 

Women 

Totals 



Horseshoe- Visual 64666 
Horseshoe-Motor 33366 


28 
21 


Nails- Visual 
Nails-Motor 


19 5 7 27 13 
10 5 13 40 16 


7i 
84 


Keys- Visual 
Keys-Motor 


23 27 26 118 105 

73 55 35 44 67 


299 

274 



>jt >j< ;j< >j< % % 

TABLE 23. 

Men 



Totals 



Horseshoe- Visual 5 6 10 6 3 
Horseshoe-Motor 3723s 


30 
20 


Nails-Visual 
Nails-Motor 


7 27 6 4 18 
50 (6) 16 (6) 27 31 7 


62 
131 


Keys- Visual 
Keys-Motor 


24 37 21 23 37 
29 43 12 22 26 


142 

132 



(5) The time totals of these records may be summarized thus: (a) As 
to puzzles — Horseshoe ; visual 58 seconds, motor 41 : Nails ; Visual 133, 



81 



motor 215: Keys; visual 441, motor 406. (b) As to sex — Women, total 
on all puzzles, visual 398, motor 379, total time for women JJJ ; Men, 
visual 234, motor 283, total for men 517. (c) As to methods of learn- 
ing — total time on visual learning, 632 seconds ; total time on motor 
learning, 662 seconds. 

(6) Concerning these totals, we may remark, (a) the men worked, 
on the whole, more quickly than the women. (b) Aside from this 
there is no general sex difference' apparent — in those puzzles where the 
men's motor time was greater than their visual time the women's 
record agrees, and vice versa, (c) The most significant result is that 
having to do with the comparative times of the two methods of learn- 
ing. With both men and women in the two simpler puzzles (horseshoes 
and nails) the visual method leads by a safe margin, but, on the other 
hand, the more difficult puzzle (ke}'s) is solved quicker by both sexes 
after motor learning than after visual learning. 

(7) A slight variation was introduced in the cases of the first and 
third male reagents on the motor learning of the nail puzzle. The figures 
there found in parenthesis indicate the time required to work the puzzle 
a second time, following their successful working with motor plus 
visual activity. These secondary figures represent such a great gain 
in time as to suggest the conclusion that the value of the combined visual 
and motor methods is decidedly more than twice as great as the value 
of either of those methods separately. 

E. PUZZLE DIFFERENCES. 
Based on the Real Experiments. 

Brief note should be made of what might be called individual differ- 
ences among these 11 puzzles. 

(1) A comparison of the different puzzle records by the same reagent 
shows immediately that the puzzles differed considerably among them- 
selves as to ease or difficulty of solution. Some were worked in 3 or 
4 seconds, others required several hundred seconds, and others still 
completely baffled the same reagent until instructions were given him. 
This wide range in the difficulty of the puzzles goes toward increasing 
the value of results in methods of learning. According to Mill's "method 
of agreement" all irrelevant circumstances should differ as much as pos- 
sible. 

82 



(2) It is interesting to note that there were only three puzzles 
which one or more of the eleven reagents failed to solve without di- 
rections. These are Nos. VII, VIII and IX. Puzzle No. IX, the 
horseshoe puzzle, is the simplest of the three metal puzzles and is ex- 
tremely easy to work. The other two puzzles, Nos. VII and VIII are 
the two maze puzzles. These evidently belong to quite a different class 
from the other 7 puzzles. All one needs with the maze is to keep at 
his task and to mark a record of his path so as gradually to discover 
where he went wrong and where right. The time element in this group 
of puzzles is therefore the only significant feature. 

(3) The puzzle of possibly greatest interest is Puzzle II, the 
second match puzzle. It seems impossible to reduce the results on this 
puzzle to any law. This puzzle was done without instructions by the 
three young women, Mm, Mt and Mg, by the bright boy Bb, and by 
the dull boy Db — not a very homogeneous group. All the other re- 
agents failed to do it without directions. In the case of the college 
graduate Ba, it was the only puzzle of the 11 in which he failed. More- 
over after the first instructions he failed again. Pd failed at first, then 
took 58 seconds to do it after the first instructions before suddenly 
dropping to his physiological limit on the third trial. Gm, the 70 year 
old reagent, failed the first two times, worked the puzzle in 80 seconds 
on the third attempt, then failed twice more, but succeeded in 18 seconds 
on the sixth try. The retarded development reagent failed repeatedly 
six times on this puzzle, then worked it twice, in 26 and 9 seconds re- 
spectively. The bright girl, Bg, failed three times in succession, worked 
the puzzle on the fourth try in only 4 seconds, but at the fifth attempt 
required 45 seconds to find her solution. There is no other puzzle com- 
ing anywhere near Puzzle II in this lawlessness. One feature of the 
difficulty in this puzzle arose from my practice of turning it bodily 
around 90 degrees after each successful working. This broke up simple 
visualizing and threw the reagent back largely on the principle involved. 
But this feature alone is not sufficient to explain the seeming irrationality 
of the puzzle. Further and more extensive experiments with this par- 
ticular puzzle would quite probably disclose some law underlying its 
variations. 

(4) On the whole a careful study of the tables of results leads 
me to prefer the two more difficult metal puzzles, Nos. X and XI, for 
producing the most satisfactory results in the testing of the learning 

83 



process. These puzzles possess at least the following desirable features : 
(a) A good degree of difficulty without instructions. A number of the 
reagents failed at first in one or both of these puzzles, (b) A solution 
consisting of several steps or movements, and this requiring a reasonable 
degree of application in order to master it. (c) The possibility of a very 
low physiological limit. This makes it possible to demonstrate promptly 
when the principle of the puzzle has been thoroughly grasped : the 
element of practice enters in but little. 

F. CONTROL EXPERIMENTS. 

(i) It remains to call attention to the control experiments. The 
time for this control series is indicated by figures in parenthesis on 
the foregoing reagent tables. On the whole there is a most satisfactory 
relation between the detail results of the control series and of the series 
of real experiments. This serves to give substantial and representative 
value to the figures in the real series, showing that they follow normal 
lines and are not controlled by any inexplicable caprice. 

(2) Attention may be called, in passing, to an interesting feature 
arising from the time results in the control series. A careful study of 
these records in comparison with the records of the real series will 
serve to substantiate practically every item of individual difference 
among the reagents, as discussed above. The dullness of the retarded 
development reagent, Rd, is again revealed ; the unexpectedly slow time 
of the Doctor of Philosophy, Pd ; the keenness of Db, the incorrigible 
boy and hopeless student ; the general normal records of the three middle- 
aged women, Mg, Mm and Mt; and the exceptional quickness of the 
6 year old boy, Sb — all of these features are nearly as pronounced in the 
records of the control series as in those of the real series. 

(3) The control series, moreover, furnishes a standardized basis for 
a comparative study of memory or retention in these different reagents. 
A study of the records with this in view will yield several very sug- 
gestive results. Let it suffice for our present purposes to call attention 
to but one item, that having to do especially with methods of learning. 
If in the control series we take the total time required first to solve each 
puzzle by all reagents who mastered that particular puzzle in the real 
series by a gradual learning, we find the average time at which the puzzles 
were first solved in the control series is 63 seconds. Over against this 
a computation entirely similar except composed of the records of those 

84 



who in the real series mastered the puzzle suddenly, rather than gradually, 
gives an average of 36 seconds. So far as it goes, this seems to indicate 
that those who originally came to a mastery of their puzzle suddenly 
retain the ability of working that puzzle again after a seven day period 
about twice as well as those who originally learned their puzzle gradually. 



85 



CHAPTER V. 

CONCLUDING DISCUSSION. 
COMPARISONS AND RESULTS. 

The foregoing discussion of results has covered many points and ap- 
proached conclusions quite frequently. Let us now endeavor to sum 
up in a few brief sentences those leading conclusions arising from this 
investigation which seem to be abundantly borne out by the data thus 
obtained, leaving untouched many of the minor or not thoroughly sub- 
stantiated conclusions suggested by the preceding discussion. It may be 
said then — 

(i) That there are great differences among puzzles, and when puz- 
zles are used for the investigation of mental features they need to be 
carefully selected, and if possible several puzzles of different types 
should be used at the same time. 

(2) The use of puzzles reveals striking personal differences among 
individuals. The differences thus discovered are frequently quite un- 
suspected, not being apparent to the ordinary observer. 

(3) Puzzles guide the way to a grouping of individuals on a basis 
of what may be called one kind of intelligence — not book knowledge, 
nor school intelligence, but the readiness with which one adjusts him- 
self to and masters a strange situation all the factors of which are within 
his control. This mental power is fairly fundamental to the general 
activities of life. 

(4) The most efficient way of learning to do a strange thing is the 
combined motor-visual method consisting of the experience of actually 
doing the thing correctly, under guidance, thus coordinating motor with 
visual impressions. 

(5) Those motor experiences are best retained which come first to 
the mind in the form of a rather sudden and hence somewhat in- 
tense experience. 

86 



(6) There is little difference in the learning value of pure visual as 
compared with pure motor impressions, although the value of the latter 
tends to rise as the complexity of the mechanical problem increases. 

When these conclusions are compared with Dr. Ruger's work there 
is found some discrepancy but no real contradiction. The discrepancy 
arises largely from the fact that the two problems do not exactly coin- 
cide. While there is much in common between Dr. Ruger's monograph 
and this present paper, there are differences of point of view and of 
method. Ruger used only one method, with no control experiments : 
the present investigation makes use of five methods in the real series 
fully repeated in a control series. Again, Ruger endeavored to peer into 
the subjective workings of the human mind when dominated by the puz- 
zle consciousness, while the present study places much emphasis on 
objective methods of learning, in an effort to discover what are the 
most economical and therefore the most efficient means of bringing the 
mind to a mastery of a normal problem-situation. For these, as well as 
for other reasons, each of these two sets of conclusions has certain sec- 
tions peculiar to itself. 

As to those portions of the field possessed in common by these two 
researches there is fair agreement. Ruger found great individual varia- 
tions : so do I ; but I would not make the differences as arbitrary and 
lawless as he seemed inclined to do. Ruger touched the question of 
grading "intelligence" by the use of puzzles : I go much further into 
this problem, but at the same time I restrict the scope of the intelligence 
thus tested. Ruger concludes that the most efficient method consists 
of analysis and the adoption of new hypotheses. So far as my intro- 
spective reports extend and so far as they can be trusted they point 
in the same direction, although not with satisfactory certainty. Prac- 
tically none of my reagents furnished corroborated testimony of having 
seen clear through any but the very simplest of the puzzles. Here 
Ruger's reports are more definite, but, being purely introspective, we 
do not know to what extent we can trust them. In those portions of 
my work which do not parallel Dr. Ruger's investigation, chiefly those 
having to do with the relative values of different methods of learning — 
auditory, visual, motor, etc., and those touching the relative permanence 
of sudden as compared with gradual acquisitions — in these and other 
unique sections of the present study there is nothing that necessarily con- 

87 



tradicts any of the results obtained by Dr. Ruger. My conclusion as 
to the longer retention of those experiences which first come suddenly 
to the mind is in harmony with the generally accepted notions of the 
greater permanence of intense impressions and the greater usefulness 
of vigorous beginnings in the formation of habit. 



(i) This report ought not to close without embodying a few practical 
pedagogical suggestions rising out of the foregoing investigation. It may 
be said then, first that the teacher will do well to watch, preferably by 
means of puzzle tests, for those individual differences among his pupils 
which may very likely represent different capacities for learning. The 
pupil truly retarded will show it in these tests ; while more than one 
who is poor at books may be discovered to be very quick at other forms 
of learning. Such an one is therefore still thoroughly teachable, the 
problem is, to get at him in the right way. 

(2) And as to what way is the right way may also be suggested 
by puzzles. Set him to a concrete task in which the motor element 
figures prominently and see if he does not find a way out. This idea 
can surely be carried over in some form or another into the routine 
teaching process. 

(3) Another profitable line of application could be based upon the 
demonstrated superiority of the coordinated visual-motor process. If the 
instruction to be imparted in the school could be cast into this form the 
mastery of the situation would unquestionably be hastened and made 
more permanent. 

(4) It may also well repay the teacher to follow out the idea sug- 
gested by the high retention-value of sudden as compared with gradual 
masteries. 

(5) Again, the very form of puzzle-learning is suggestive. It in- 
volves the recognition of a definite problem. Now if the teacher can 
bring his pupils to see that the morrow's lesson, for instance, is their 
problem and that they are to work this out as much as possible for them- 
selves, great pedagogical gain will unquestionably be made. As far as 
possible let each pupil discover in connection with coming instruction 
his own problem. Give him some liberty of choice. Allow for individual 
differences in interest. Then when he has found his problem and feels 
that it is his let him work out its solution somewhat in his own way 

88 



and as far as he will on the strength of his own initiative. This is good 
teaching. This also is puzzle-learning in another form. 

(6) One thought remains, it grows out of the great difference be- 
tween what we may call the school-rating or book-learning rating of 
reagents, on the one hand, and their rating in the solving of puzzles, on 
the other. It is a tair question to ask: Which represents a better equip- 
ment for meeting the ordinary situations of real life? Now if all 
students were to become teachers or professors, our answer would be 
immediate, and in favor of book-learning. But when one looks out 
over the life if men and women in general, he can not help pausing 
thoughttully as he asks himself such a question as the above. Are our 
schools loading up boys and girls with an accumulation of learning 
which is largely conventional, and this to the exclusion of opportunities 
for development along lines of practical and motor response? If so, 
is this best? If it is the function of the school to prepare for citizenship; 
to prepare lor life ; to fit one to be the best possible member of the 
body politic, to contribute the most possible to the economic whole, 
to help '.reate and maintain the highest possible type of the family, 
to himself attain and to help others attain the largest possible form 
of self-realization — if this is the function of the school, is the school 
using the best means to accomplish this most practical and far-reaching 
end? All this may seem a long remove from the pyschology of puzzle- 
learning, but as a matter of fact it springs out of our present investigation 
of several points. To indicate but one, let us remind ourselves of Db, 
classified by the school system with which he had been in contact as a 
"reject." Incorrigible in conduct, hopeless in books, he was turned out 
and away. But in puzzle-learning he clearly outstripped all my other 
reagents and all but two of them (the small boy and the 70 year old 
woman) were unquestionably his superiors in schooling. Has the school 
nothing more for such a promising case? Is it taken for granted that he 
can never be a valuable citizen because he fails to meet certain academic 
requirements? Must he continue his training for life either on the 
street or under certain conditions of self-depressing social disapproval, 
tagged as hopeless if not harmful? There is far better stuff in this 
boy than the system can give recognition to. But one cheering sign of 
the times is the movement already under way to include such promis- 
ing but irregular cases within the scope of the school's preparation for 

8q 



effective functioning as citizens in an enlightened state. A beginning 
has been made, but much yet remains to be done. 

The foregoing investigation while it has answered some questions 
has raised new ones : for every problem to which it offers a solution 
it calls attention to some other problem demanding further research. 
It may be well, in closing, to note some of these suggestions for further 
study arising out of the work here reported. 

(i) As to Pd's unexpectedly slow work with puzzles — is it due to a 
native weakness along this line, or did he once possess good puzzle 
ability which has been lost through years of abstract thinking? Is 
this true of all similar cases? 

(2) If this second alternative is not the true one with Pd, and for 
some reasons I am inclined to believe it is not, did Pd ever possess 
those qualities of mind which made it possible for him to master for 
himself new situations in any of the realms of learning? Was he ever 
an original thinker, a real discoverer? Or was he a man with but a 
good rote memory, easily able to accumulate and retain many facts, but 
lacking in fundamental strength of all inventive powers? Could he 
see and remember a thing in many relationships, when they were 
pointed out to him, while yet unable to seize upon new relations for 
himself? Did he always lack the critical and the creative mind? Does 
his record in puzzles indicate this? For a number of personal reasons 
I so believe. The wider problem is — can puzzles be trusted to reveal the 
native presence or absence of this particular form of mental power in 
any or all persons properly tested? 

(3) As to the small boy, Sb, should we find his unusual readiness 
to work puzzles indicating a type of mind which can readily grasp mathe- 
matical forms and processes — and would not this hold true of all such 
cases? 

(4) Should we not find that all instances of school dullness ac- 
companied by totally unsuspected puzzle brightness, such as we have in 
Db, would respond vigorously to various difficult forms of learning in 
connection with the manual arts? 

(5) Does it hold true universally that for simpler motor processes 
pure visual presentation is more effective than pure kinesthetic, while 
as the processes increase in complexity the kinesthetic presentation soon 
comes to lead all others as a method of learning? 

90 



(6) If so, can this principle be transferred to other than material 
subject matter, so that in abstract subjects and in the realm of pure ideas, 
the greatest economy of learning can be achieved by the use of the 
kinesthetic presentation, if such can be devised? 

(7) One of the most interesting studies suggested by this research 
would be in introspection. Can not introspection itself be made the sub- 
ject of experimental investigation? And if so, should we not reach funda- 
mentally valuable results by a careful study, of, for instance, free in- 
trospection compared with controlled introspection? 

These among others are problems calling for further research. 



91 



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